Everton became the fourth side to win at Upton Park this season and, despite improvement in the second half, West Ham could have no real complaints about this 1-0 loss.
New 17-year-old sensation Wayne Rooney did not emerge from the subs' bench until early in the second half but this time it was midfielder Lee Carsley who grabbed the winner for Everton.
He climbed above Scott Minto at the far post to head former Hammer David Unsworth's high, hanging cross powerfully past David James in the 70th minute.
James decided against coming for the cross, which swirled in the gale force winds that swept around the Boleyn Ground, and was perhaps mindful of his error that nearly presented the Toffees with the lead just before the interval, when Li Tie nipped in behind the West Ham keeper but could only divert his shot wide of the far post from a very tight angle.
To be fair to James, though, he had earlier denied Kevin Campbell with a point blank save from 12 yards.
At the other end, Richard Wright had little to do, especially in the first half. Apart from parrying efforts from Trevor Sinclair and Jermain Defoe at the start and finish of the half, the only other save he had to make was to gather a speculative 25-yarder from Minto. It was a turgid first 45 minutes and the crowd - as well as those watching at home on Sky TV - had a right to expect more entertainment and a higher tempo from the hosts.
After wins at Fulham and Sunderland in the past eight days, though, Hammers never got into their stride. The defence has been fairly criticised for previous defeats at home but the back four were steady enough for most of this afternoon and it is now the lack of goals that must also concern manager Glenn Roeder. West Ham have failed to score in four of their six home games and while they took the game more to Everton in the second half, they were unable to finish several good openings.
Defoe, often an isolated figure as Paolo Di Canio drifted wide to the flanks, had little chance to shine, although, perhaps significantly, his best openings came after Titi Camara replaced Minto and added more presence to an otherwise lightweight attack that is missing the injured Fredi Kanoute.
Although not as effective as in previous home games, Joe Cole looked a threat when he moved in from his wide position on the right and one amazing dribble near the by-line produced a rasping shot that Wright saved at the near post. Maybe Cole would cause the opposition more headaches if released to play a less constrained role behind the front two?
At least the quality of crossing showed improvement today, but Ian Pearce was unlucky to head Di Canio's corner into the side-netting at the Bobby Moore Stand end, while Edouard Cisse (a second half replacement for the returning Steve Lomas) could only prod another left-wing cross from the Italian at Wright. Sinclair's late, mishit volley at the far post summed up another grey afternoon in East London.
With a daunting trip to Liverpool now facing the Hammers, the hope is that our excellent away form of late will continue as we search for our first win at Anfield in almost 40 years that would provide a huge confidence boost as we prepare for three consecutive home games in November against Oldham (Worthington Cup), Leeds United and Manchester United.
Minute-by-minute:
2 - Pembridge plays a short pass to Campbell on the edge of the area and sprints to collect the return but James is quickly off his line to snuff out the danger.
3 - Cole's gains possession on the left and curls in a cross that Lomas flicks on to the far post for Sinclair, whose right-foot volley is superbly tipped round the post by Wright.
23 - Cole's measured pass finds the overlapping Minto, whose driven cross is too pacy for Sinclair as he bursts into the six-yard box.
27 - Everton are presented with the best chance of the match so far, as Hibbert's clever through-ball catches out Pearce and leaves Campbell in the clear just eight yards out. However, James comes to the rescue, throwing himself in front of the ball to block the striker's effort.
31 - Carrick lays an inviting pass square for Minto, who collects the ball some 25 yards out and fires in a fierce shot that Wright holds well with Di Canio ready to pounce on any rebound.
35 - Ian Pearce is just inches away from connecting with Di Canio's dangerous free-kick on the right as Yobo rises to clear the ball.
38 - Hibbert's swerving effort from 25 yards out catches the wind and almost deceives James, who parries the shot and then does well to gather the loose ball before Campbell can strike.
40 - Cole's neat touch puts Defoe in on the right, but the striker's low shot is blocked by Wright and Unsworth clears.
44 - A mix-up in the Hammers defence almost gifts Everton the lead, as a hopeful chip into the penalty area sees Li Tie burst through and James completely misses the ball as he attempts to punch clear. However, the Chinese midfielder can only sweep the ball across the six-yard box from an acute angle and it runs out of play for a throw-in.
Added time: 1 minute.
Half-time: West Ham United 0 Everton 0.
Second half:
46 - Everton on the attack immediately, as Radzinski plays in Pembridge, whose low left-foot shot is blocked by Lomas in the six-yard box.
51 - Cole latches on to Sinclair's pass into the penalty area but can only toe-poke the ball into the arms of Wright as Yobo comes across to make a challenge.
57 - Carsley's free-kick from the left is met by the head of Kevin Campbell on the edge of the six-yard box, but the effort thankfully loops over the bar as James clatters into the striker.
59 - Di Canio's corner from the east side is met by Pearce at the near post, whose header has the Dr Martens Stand cheering as it hits the net - only for the crowd to then realise it has crashed into the wrong side!
60 - Cole's low cross finds its way through to the unmarked Di Canio just eight yards out, but the Italian fails to connect properly with his effort and Wright easily collects.
65 - Substitute for Everton, Rooney replaces Radzinski.
67 - Rooney almost makes an immediate impact as he races on to Campbell's through ball and holds off Dailly, but clips his shot just over the bar.
70 - GOAL. After threatening dangerously for the previous five minutes, Everton find a breakthrough, as Unsworth's deep cross from the left is met by Carsley at the far post, who rises above Minto to power a header past James at his near post. West Ham United 0 Everton 1.
74 - Substitution for West Ham, Cisse replaces Lomas.
76 - Cisse gains possession on the right and sends over an inviting cross that drops perfectly for Sinclair, but he directs his header up and over the bar from six yards out.
81 - Tremendous determination from Cole almost pays off as he wins possession in what looks like a lost cause on the edge of the penalty area, jinks past two defenders and fires in a shot to the near post that is well turned round by Wright.
82 - From Di Canio's corner, Cole volleys goalwards from the edge of the penalty area but the effort is deflected wide for another corner.
83 - Substitution for West Ham, Camara replaces Minto.
87 - Camara races down the right before cutting inside before slipping the ball through to Defoe, who slices his shot high and wide from 10 yards out.
88 - With Hammers throwing men forward in desperate search of an equaliser, Everton break in numbers as Carrick's free-kick goes wrong. Pembridge sets up Campbell, whose right-foot shot is deflected wide for a corner.
90 - Substitution for Everton, Pistone replaces Tie.
Added time: 3 minutes.
90 - Defoe finds a yard of space on the edge of the area, and his fizzing shot takes a wicked deflection but is held by the grounded Wright.
90 - Di Canio clips the ball into the danger area in a last throw of the dice, but Cisse's acrobatic effort is saved by Wright.
Full-time: West Ham United 0 Everton 1.