Goals from Don Hutchison, Paolo Di Canio and Frederic Kanoute helped secure a convincing win in front of the live Sky TV cameras and lifted the Hammers off the bottom of the Premiership table up to 15th place, above Charlton, Ipswich, Derby, Leicester and Southampton.
While the result and overall team performance will have provided the biggest boost for Roeder, the individual displays of Hutchison and Tomas Repka - making their home debuts for the club - were also highly encouraging.
Hutchison controlled the midfield with fellow Geordie Michael Carrick, while Repka kept Alan Shearer quiet for most of the game and defended solidly alongside Christian Dailly.
While Newcastle had their moments in an entertaining match, it was the hosts who dictated the majority of the play and the attacking force provided by the likes of Hutchison, Carrick, Sinclair, Di Canio and a fit Frederic Kanoute proved too strong for the Magpies defence.
If only that attacking line-up had been in place for the entirety of the previous five league matches, the Hammers' current league position would surely be even higher.
The opening goal owed much to the initiative of another impressive home debutant, French winger Laurent Courtois, who rushed over to collect a short corner from Di Canio in the 18th minute and whipped in a dangerous left-footed cross that was met with a powerful low header from Hutchison that flew into the net to silence the travelling Geordie support.
There was also a slice of irony about the goal - it was the second time that Hutch had scored against his boyhood idols on his home debut for the Hammers after he notched a consolation from the penalty spot back in August 1994 during a 3-1 defeat.
This time around, however, the end result was to prove much more satisfying for Hutchison and his new team-mates.
The Hammers came out for the second-half in similarly determined mood and almost added another just two minutes in, as Kanoute's cross appeared to be dropping perfectly for Di Canio, until a defender cleared at the vital moment.
Six minutes later, however, the Italian striker was celebrating as his luck in front of goal changed. A searching long pass from Dailly dropped at the feet of Di Canio on the left and, faced with just the injured Warren Barton between him and the Newcastle goal, ran at his marker before turning on to his left foot and firing a low shot past the outstretched arm of Given.
That gave the Hammers the cushion they needed to be even more confident on the ball and the crowd and watching millions at home were kept entertained as Di Canio, Kanoute and Sinclair brought out their repertoire of tricks and flicks to further bamboozle the Newcastle defence.
The fancy footwork wasn't just for show, though, and a Di Canio special created the third and final goal with eight minutes left. Collecting a Sinclair throw on the right, he instinctively back-heeled the ball to Hutchison on the edge of the area, and the Hammers midfielder shielded the ball from Rob Lee to allow Kanoute a free run on goal.
The Frenchman confidently tucked the ball under Given for his first goal of the season and that long-waited opening victory was virtually secure.
On this kind of showing, the Hammers should be in for an exciting season, providing they can add more consistency and goals away from home, and boss Roeder admitted afterwards that he certainly wouldn't be getting carried away with the afternoon's events.
He said: "I'm pleased for everyone at the club today, from the players, the coaches and the fans, right through to the tea lady, because everyone here has worked hard to make the team successful and it is nice to get our first win in style.
"There is still a long way to go, however, and we will carry on working hard to ensure that we can produce that kind of performance as often as possible.
"It is very important to me that we keep everyone fit, because the squad is so small and we can't afford to be without our best players - the front two especially. Fredi Kanoute was magnificent today, he gives us something different and his presence up front is matched by his technical ability.
"Paolo is just Paolo. His skills were exquisite and his goal was typical. People in the media are still trying to suggest that there are problems between Paolo and the club, or between Paolo and me, or even between Paolo and the players. But I find it strange to understand because I certainly haven't noticed any problems, or the so-called 'fall-outs' that are apparently occurring at the training ground.
"The players here all get on and are working hard together. Paolo speaks his mind - we have always known that and it is not a problem here at all."
Glenn also had words of praise for his debutants, and insisted that it wasn't only the attacking prowess that pleased him today.
"We scored three and played so well in the attacking third but just as important was the clean sheet we kept at the other end. Repka looked solid alongside Dailly and we kept a good shape all over the field. The boys in midfield played well and I am very excited about the partnership between Carrick and Hutchison.
"I was also pleased with the little lad Laurent Courtois, who came on a free transfer from Toulouse in the summer. He didn't let us down and contributed well to the performance."
The only low point currently facing the Hammers boss is the concern over Joe Cole's fitness. The England starlet was forced to sit out today's match after again aggravating the foot injury he originally sustained nine weeks ago at the start of the pre-season campaign, and Glenn admitted it may take some time before he is back to full fitness.
"Joe has been quite frustrated with the injury and it is clear that the problem hasn't healed fully. We have decided that the best course of action will be to rest him for a little longer and see how things progress from there.
"He is too valuable to us, so we won't be risking him until we are sure he is fully healed. Hopefully he will be back soon, but Laurent has already proved that we have a more than able replacement on the left."
There will no doubt be a few Premiership defenders losing sleep when Cole does return to link up with the likes of Di Canio, Sinclair, Kanoute, Carrick and Hutchison, but things are certainly starting to take shape under the Roeder revolution.
Newcastle have now lost their last 26 matches on their travels in London, and the Hammers' next task will be to face Everton next Saturday at Goodison Park, where their record in recent years is almost as poor.
Confidence certainly won't be lacking after today's performance, though, and let's hope that our first victory of the season is the start of things to come…
www.whufc.com man of the match: Sebastien Schemmel: Kept Newcastle's danger-man - Laurent Robert - quiet for the majority of the match and also found the time and energy to get forward at every possible opportunity to link impressively with Sinclair and Kanoute down the right.
By Danny Francis
Minute-by-minute:
3 - Elliott goes down in the penalty area under the challenge of Dailly, but referee Peter Jones waves away the Geordie claims for a spot-kick.
9 - A flowing move down the right sets Sinclair away but his cross is too deep for Kanoute and Courtois.
11 - Courtois finds Di Canio on the left and the Italian's shot is only parried by Given, but Carrick can't find the all-important touch.
14 - A foul on Kanoute presents the Hammers with a good opportunity some 25 yards out but Di Canio's clip into the area isn't anticipated by Courtois.
18 - GOAL! Di Canio plays a short corner on the right to Courtois, who's near-post cross is met by a diving Hutchison, who heads past Given from six yards out for his first goal since returning to Upton Park and West Ham's first in open play this season. West Ham United 1 Newcastle 0 United.
19 - Laurent Robert's free-kick from the left is headed just over the bar by Shearer.
21 - Di Canio's corner from the left is met by Sinclair, who's effort is cleared off the line by Elliott. Dailly's follow-up is then deflected wide off Sinclair for a goal-kick.
24 - Dailly misjudges Barton's long pass and Bellamy nips in behind Repka but sees Hislop tip his effort over the bar.
26 - Robert skips past Schemmel on the left and whips in a dangerous low cross that Hutchison does well to flick over the bar for a corner.
30 - Another Di Canio corner from the left causes panic in the Newcastle defence as the ball is flicked on to the far post where Repka volleys high over the bar from 10 yards out.
31 - Carrick denies Bellamy just inside the right-hand side of the penalty area with a perfectly-timed sliding challenge.
35 - Kanoute's low cross from the right looks like reaching Di Canio until O'Brien clears the danger.
36 - Kanoute again breaks the offside trap and cuts inside from the right before firing in a shot that is blocked by Given. Di Canio hooks the rebound wide.
41 - Shearer's flick-on finds Bellamy, who's low cross is met by Robert, but the Frenchman scuffs his shot into the arms of Hislop.
42 - Kanoute finds Sinclair on the right and the winger takes one touch before firing in a blistering shot that flies just inches wide of the top corner.
45 - Robert whips in a low corner from the left that is met by Elliott, whose effort is saved well by Hislop.
Added time: 2 minutes.
Half-time: West Ham United 1 Newcastle United 0.
Second-half:
47 - Almost a goal from West Ham's first attack of the half, as Kanoute wriggles free inside the area and loops over a cross that looks like falling perfectly for Di Canio until a defender touches the ball away from his path. Courtois volleys the loose ball high and wide.
53 - GOAL! Dailly's measure long ball out of defence finds Di Canio wide on the left. The Italian maestro turns Barton before firing a low left-foot shot past Given from 10 yards out. West Ham United 2 Newcastle United 0.
56 - Lee's pass is headed into the area by Solano, where Acuna is waiting to lift the ball over Hislop. Repka clears the danger as the ball runs loose.
57 - A Robert corner is met by O'Brien, whose header is flying in the top corner until Courtois heads off the line.
58 - Substitution for Newcastle, Distin replaces Barton.
59 - Winterburn booked for foul on Solano.
65 - Shaka Hislop's long kick clears the Newcastle defence and sets Di Canio away, but the striker wastes the chance to kill the game off as his attempted lob drops into the arms of Given.
69 - Di Canio sprays a corner to Carrick on the edge of the area but the England midfielder's fierce first-time volley is blocked by Shearer.
70 - Schemmel booked for a foul on Lee.
73 - Another blistering volley, this time from Kanoute, is blocked by Lee.
74 - Schemmel skips down the right and pulls the ball back for Kanoute, whose first time effort is magnificently tipped round the post by Given.
76 - Substitution for Newcastle, Ameobi replaces Solano.
80 - Di Canio's cross from the left is headed over by Kanoute from six yards out.
82 - GOAL! Sinclair's quick throw is impudently flicked on by Di Canio to Hutchison, who shields the ball from the defender, allowing Kanoute to run through and calmly slot the ball under Given for his first goal of the season. West Ham United 3 Newcastle United 0.
83 - Substitution for West Ham, Defoe replaces Kanoute.
87 - Substitution for West Ham, Moncur replaces Courtois.
88 - Moncur booked for foul on Ameobi.
Added-time: 2 minutes.
90 - Carrick floats in a cross that is met by the head of Hutchison, but Given turns the effort round the post.
Full-time: West Ham United 3 Newcastle United 0.
Report and reaction to follow...