Jack Collison scored the only goal of the game for West Ham as Manchester City's miserable away form continued at Upton Park.
The young midfielder was on hand to lob the ball home in the 71st minute after Shay Given could only parry Savio's curling effort from the left corner of the penalty area.
But the Hammers' day was marred by a serious injury to Valon Behrami, who was carried off in obvious pain in the first half after catching his studs in the turf as he challenged Wayne Bridge, badly twisting his ankle and knee.
Robinho saw one first-half effort superbly saved by Rob Green, before missing a glorious opportunity at the far post when he stabbed wide after good work from Stephen Ireland and Craig Bellamy.
Former Hammers striker Bellamy, jeered by the home fans on his return to Upton Park, was replaced by Elano in the 66th minute, with the Brazilian seeing a late free-kick glanced onto the outside of the post by Lucas Neill.
Herita Ilunga almost created a breakthrough after eight minutes, cutting inside his man and curling a low ball into the penalty area.
Carlton Cole was the target but he was just unable to make a connection and Given collected comfortably.
Two minutes later, former Hammer Bellamy found space for the first time and floated a cross towards the far post, forcing a corner.
Scott Parker, meanwhile, earned a 10th minute booking for a reckless challenge on Micah Richards. The England man left the field minutes later in favour of striker Felipe Caicedo, forcing a reshuffle.
After 14 minutes, Robinho almost had the ball in the net from the daintiest of touches. A mistake by Matthew Upson gifted Ireland possession and when his cross was cleared Vincent Kompany volleyed for goal.
His shot was weak but Robinho, given onside, flicked his boot at the ball and almost succeeded in steering it past the sprawling Green.
The Brazilian then missed a sitter in the 22nd minute. The hard-working Bellamy was the architect, breaking free on the left byline before cutting the ball across goal for Ireland.
The midfielder dragged it first time to the far post where it fell to Robinho, who missed the target from just two yards.
West Ham had the chance to reverse the pressure with a free-kick in a dangerous position but Radoslav Kovac, on his full home debut, headed high and wide from David Di Michele's fine delivery.
With half an hour gone, a swift break from Behrami created a shooting chance for Cole but he dallied over his attempt and ended up blazing over.
It was Behrami's last contribution before leaving the pitch on a stretcher having twisted his knee attempting a tackle.
But the Hammers continued to press, with Given again called upon when Di Michele hit a firm shot from 10 yards following some superb approach play around the City area.
Just 90 seconds after the restart Collison was inches away from capping a fine West Ham move with the opener. The Wales international started the attack with some good, aggressive running, before passing to Cole and continuing his run.
Cole found Di Michele with a crisp first touch and the latter's cross curled invitingly towards Collison. The angle was tough and he just failed to connect with an attempted volley and the danger was cleared.
City fed the ball to Robinho on the right but, despite some customary stepovers, the enigmatic forward remained short on inspiration.
Indeed, the hosts were still playing the better football, with another pacy attack - this time set in motion by Ilunga's neat back-heel - ending with Parker's goal-bound shot being charged down.
Robinho's disappointing day took another downturn in the 63rd-minute when he took responsibility for an inviting free-kick and promptly drove his effort straight into the stands.
The home side's failure to create something clear-cut must have frustrated the fans but, predictably, Bellamy's substitution with 25 minutes to play gave them something to cheer.