Chelsea's victory momentarily gave them a four-point lead at the summit, but Arsenal closed the gap to a point by overwhelming Sunderland 4-1 and City are three points back with a game in hand after edging Stoke City 1-0.
The former Montpellier man also played a role in the glorious move that led to Tomas Rosicky chipping in Arsenal's third goal before half-time, with Laurent Koscielny heading home a fourth in the 57th minute.
Emanuele Giaccherini claimed a late consolation for Gus Poyet's side, who face City in next weekend's League Cup final.
City also tasted Champions League disappointment in mid-week, losing 2-0 at home to Barcelona, and their return to winning ways was not quite as straightforward as Arsenal's.
Manuel Pellegrini's side toiled in front of goal against Stoke at the Etihad Stadium and there was a sense of relief when Yaya Toure broke the deadlock from Aleksandar Kolarov's cut-back in the 70th minute.
With Everton goalkeeper Tim Howard in sparkling form, Chelsea looked set to drop points until Terry marked his return to the team after a three-game absence by toeing home a Frank Lampard free-kick in the 93rd minute.
Terry's strike was a bitter blow for an enterprising Everton side, who squandered an opportunity to close the eight-point gap that currently separates them from fourth-place Liverpool.
Robin van Persie opened the scoring at Selhurst Park with a 62nd-minute penalty after Marouane Chamakh tripped Patrice Evra just inside the Palace area.
Wayne Rooney doubled United's lead six minutes later, celebrating his new five-year contract and marking his 300th league appearance for the club by slamming a half-volley into the top-right corner.
Fulham were on course to climb off the foot of the table thanks to Ashkan Dejagah's 28th-minute goal, only for Matej Vydra to plunder an 86th-minute equaliser with a shot that squirmed past Maarten Stekelenburg.
Vydra's goal meant that Cardiff City remained second from bottom after they were crushed 4-0 at home by Hull City, who prevailed through a Nikica Jelavic brace and strikes from Tom Huddlestone and Nikica Jelavic.
Hull are now six points above the relegation zone and West Ham United are a point better off in tenth place after goals from Matt Jarvis, Carlton Cole and Kevin Nolan set up a 3-1 win at home to Southampton.