Damien Duff's second-half equalizer for Fulham at Eastlands left City 10 points off league leader Manchester United, which also has a game in hand over its crosstown rival.
Mario Balotelli had put City in front in the 28th but Duff's leveler will give extra delight to Fulham manager Mark Hughes, who was fired by City 14 months ago.
West Ham beat Liverpool 3-1 in Sunday's other league match to move off the bottom of the table. The defeat ended the Reds' six-match unbeaten streak in the league, denying them the chance to move within three points of fifth-place Chelsea.
Exchanging a couple of short passes with Carlos Tevez, Balotelli was given too much room by Fulham captain Danny Murphy and put an excellent shot past Mark Schwarzer to put City in front with his ninth goal of the season.
Fulham equalized when Brede Hangeland sent Andrew Johnson down the right wing and the striker crossed to Duff, who timed it exactly right to score from close range.
City manager Roberto Mancini did not appear to look at counterpart Hughes at the post-match handshake, leading to the Fulham manager pulling his hand away.
"I am old-fashioned," Hughes said. "I always think you should offer your hand in whatever circumstances, no matter how difficult it is."
City had come into the match on the back of a 2-1 defeat to United in its last league game, and a top-four finish may well be the club's target now.
Goals by the impressive Scott Parker and Demba Ba gave West Ham a 2-0 lead at halftime against Liverpool, which improved after the break and halved the deficit through Glen Johnson in the 84th.
Carlton Cole sealed the win in stoppage time for the Hammers, who are still in the relegation zone but are now level on points with 17th-place Wolverhampton Wanderers.
"We played well, scored three and could have scored more. I'm happy," West Ham manager Avram Grant said. "This result shows the players what quality we have. We're not a team that should be down the bottom."
