After winning their first nine Premier League game at Eastlands, City have started to stutter at home having drawn their last three matches in which they have allowed six points to slip away.
City manager Sven-Goran Eriksson will have been delighted to pick up a point as his side could easily have lost and surrendered their unbeaten home record.
The Hammers, who lost 1-0 at City four days earlier in the FA Cup, completely dominated the second half and ought to have left victors, though the point they picked up consolidates their top-ten spot.
City had an early let-off when Freddie Ljungberg beat the offside trap but keeper Joe Hart dashed off his line to block at the feet of the Swede.
But they did not heed that warning as the Hammers stole ahead in the eighth minute. Richard Dunne's wayward clearance gifted possession to the visitors and Ljungberg's cross was converted by Carlton Cole.
The Hammers striker flicked the ball up and found the net with an acrobatic overhead kick, despite the valiant effort of Micah Richards to keep out the effort.
It was a sweet moment for Cole because, but for an injury to Dean Ashton, he probably would not have made the starting line-up.
City were on level terms in the 16th minute though when Darius Vassell scored his third goal of the season after some slipshod defending.
The Hammers failed to clear Martin Petrov's cross and Vassell was free inside the six-yard box to slot the ball low past keeper Robert Green.
After a lively opening quarter-of-an-hour the remainder of the first half was decidedly flat with neither side carving out any further chances.
The Hammers made a far more positive and adventurous start to the second half as Mark Noble and Cole both went close.
Hayden Mullins then brought a fine save from Hart and the same player shot just wide.
City had another let-off in the 73rd minute when substitute Julien Faubert forced home a Ljungberg cross from close range, only to have the effort ruled out for offside.
Hart then came to City's rescue again, keeping out Noble's shot with his legs.
Ljungberg twice went close to grabbing a winner in the latter stages, each time cutting in from the left but firing into the side-netting on both occasions.
Then, in the third and final minute of stoppage time, the Hammers again so nearly snatched victory through Cole's header which was brilliantly turned over the crossbar by man-of-the-match Hart.