City pulled a goal back almost instantly thanks to David Silva's strike, but they were unable to find an equaliser as the Hammers held on for the points.
Here, Sports Mole takes a closer look at the action between the two teams at Upton Park.
On target: 4
On target: 5
Was the result fair?
The statistics would suggest that Manchester City should have come away with a win, but it is hard to argue against the actual result when you consider the energy, determination and enthusiasm that West Ham showed.
West Ham's performance
Sam Allardyce will be thrilled by how his team played, with every member of the side giving 100% at all times. There was a superb level of organisation and commitment in defence, while the midfield gave City barely a moment's peace. Alex Song in particular was superb, chasing down the opposition and winning the ball back for his side on numerous occasions. Meanwhile, Enner Valencia and Diafra Sakho continued their impressive partnership in attack with a vibrant display from both. The Hammers are absolutely flying at the moment, and those who have dismissed Allardyce for negative tactics in the past must be looking on in amazement right now. It will be difficult for them to stay at this level for the rest of the season, but try telling that to their buoyant fans.
Man City's performance
The champions will feel unlucky that they did not come away with at least a point on a frustrating day in East London, but they were lacking in key areas when it mattered. Vincent Kompany and his fellow defenders frequently struggled against the likes of Valencia and Sakho, while Fernando offered little in midfield when they desperately needed some mettle. There was little to complain about up front from a creative point of view as Sergio Aguero, David Silva and Yaya Toure all carved out good chances. However, some poor finishing cost them dearly in the end. Manuel Pellegrini will not be too upset by how his players performed, though they could soon find a considerable distance between themselves and Chelsea in the table.
Sports Mole's man of the match
Alex Song: The Cameroonian was a force of nature in midfield for West Ham, covering every blade of grass in his quest to stifle Manchester City going forward. Song was brought to Upton Park for that very purpose in the summer, and this may well have been his most dominant performance yet in the claret and blue jersey.
Aguero had a glorious chance to equalise for City midway through the second half, only to see his effort rattle the crossbar from close range. The striker is up there with the best in the world and he really should be burying simple opportunities like that.
Martin Atkinson maybe gave one too many decisions Manchester City's way in the first half, but his overall display was solid enough. That said, one incident which he might be questioned about came at the end of the first half when Aguero went in studs up on West Ham captain Mark Noble. Atkinson was in the ideal position to penalise the Argentine, but he got away with it.
West Ham: The Hammers are back in Premier League action next Saturday with a trip to Stoke City.
Man City: The Blues continue the defence of their League Cup crown on Wednesday when they host Newcastle United in the fourth round.