After going six matches without a win in the Premier League, Slaven Bilic knew the importance of getting all three points and his players showed character, determination and the quality to get back on the winning trail.
The Hammers got their just rewards after dominating the first half and hitting the woodwork twice.
And it was their inspirational captain who helped them secure the victory with the crucial goal just before half-time.
Winston Reid was brought down inside the area and although Noble missed his penalty, he was on hand to fire the rebound into the back of the net.
Despite a nervy second half, the Hammers players produced a superb defensive display to keep a vital clean sheet and give them the perfect confidence boost ahead of another big home game against Hull on Saturday.
It was also the perfect way to mark tribute to former FA Cup hero Peter Brabrook who passed away this week and would have been proud of the minute's applause shown towards him by the Hammers fans just before the game.
Bilic had called for his players to show the right mentality and said this was the time that his side had to deliver and they did not let him down.
The Hammers dominated the first half proceedings and could have opened the scoring after just two minutes when Michail Antonio's cross picked out Andy Carroll and his header flew just wide of the post.
Dimitri Payet also came close on six minutes when he found space just outside the box and fired the home side's first shot on target which produced a comfortable save from Tom Heaton.
The London Stadium also paid respect to young Hammer Jack Howard who tragically passed away last week on 13 minutes with a standing ovation which seemed to inspire the home fans.
West Ham continued to dominate and had strong claims for a penalty turned down on 27 minutes after Winston Reid's header appeared to strike the hand of Burnley defender Michael Keane.
But referee Bobby Madley ignored the strong pleas from the home supporters and waved for play to continue.
It was all one-way traffic as the home side continued to mount pressure on the Burnley goal.
Payet laid the ball into the path of Pedro Obiang on 35 minutes who saw his left-foot shot strike the outside of the post.
The Hammers were denied by the woodwork once again on the stroke of half-time after Payet's short corner picked out Noble and he saw his curling right-foot shot cannon back off the post.
But the home side finally got their just rewards moments later when they broke the deadlock after Reid was brought down inside the area by Ben Mee.
Noble, who is normally so reliable from the penalty spot saw his effort saved by Heaton diving low to his left, but he made no mistake firing the rebound into the back of the net.
You could sense the relief among the Hammers players and Noble in particular who knew the importance of his match winning strike.
Bilic must have feared a response from Burnley in the second half and that proved to be the case as they had several opportunities to grab an equaliser, but they could not find a way past the Hammers defence and the superb Darren Randolph in the West Ham goal.
Burnley's first attempt on goal came on 51 minutes when a deep free-kick into the ball fell to Vokes who struck an over-head kick and his effort flew just wide of the post.
Arfield then saw his cross palmed away by Randolph on the hour mark straight into the path of Vokes who had the goal at his mercy but he headed the ball over the bar.
Randolph showed his quality once again on 71 minutes when he made a superb save diving away to his left to keep out a fierce free-kick from Arfield.
Ayew could have sealed the victory in injury time when he weaved his way into the penalty area and fired his shot inches past the post, but the Hammers held on for a crucial victory and will be hoping for more of the same when they face Hull on Saturday.
West Ham: Randolph; Nordtveit, Reid, Ogbonna; Antonio, Noble (Nordtveit 88), Obiang, Cresswell; Lanzini (Ayew 69), Carroll (Fletcher 82), Payet
Subs not used: Adrian, Fernandes, Quina, Browne
Burnley: Heaton; Lowton, Keane, Mee, Ward; Arfield, Marney, Defour, Boyd (Barnes 76); Hendrick, Vokes
Subs not used: Robinson, Flanagan, Kightly, Bamford, Defour, Tarkowski
Bookings: Mee, Hendrick
Referee: Bobby Madley