Gibson, who was often pilloried by sections of United’s supporters before he joined Everton in mid-January, did his old club a huge favour after driving in his first goal for the Toffees on 60 minutes to sink City at Goodison Park.
The match was held up for several minutes towards the end of the first half after a fan ran onto the pitch and handcuffed himself to City’s goalposts.
City’s third defeat of the season saw United join them on 54 points after a clinical 2-0 win over Stoke at Old Trafford, both goals coming from penalties.
Sir Alex Ferguson’s side took the lead with a Javier Hernandez spot-kick on 38 minutes, the Mexican international striker converting after Jermaine Pennant clattered into Park Ji-Sung.
The champions then doubled their lead with another penalty shortly after half-time, Dimitar Berbatov stroking home after Antonio Valencia had been fouled by Jonathan Walters.
Third-placed Tottenham maintained the pressure on the Manchester clubs, strolling to a 3-1 victory over Wigan at White Hart Lane.
Two goals in the space of five first-half minutes effectively sealed all three points for Spurs, Gareth Bale opening the scoring on 29 minutes after being picked out by Luka Modric.
Modric then turned scorer for Tottenham’s second, lashing past Ali Al-Habsi from 20 yards in the 34th minute as Spurs ran riot.
Bale grabbed his second midway through the second half to complete a miserable night for the Latics before James McArthur bagged a consolation goal in the 80th minute.
Tottenham’s win saw them stretch their lead over fourth-placed Chelsea, who had to dig deep to scramble a 1-1 draw with promoted Swansea.
A Neil Taylor own-goal saw Chelsea snatch an injury time equaliser, the London club had earlier been reduced to 10 men after Ashley Cole’s sending off, as the Londoners fought back after Scott Sinclair had given Swansea the lead.
Former Chelsea player Sinclair netted six minutes before half-time with a looping shot after Bosingwa failed to clear Gylfi Sigurdsson’s header.
Liverpool moved to within four points of Chelsea after Andy Carroll scored on the anniversary of his move to Anfield as the Reds maintained their recent run of form with a 3-0 win over relegation-threatened Wolves at Molineux.
Carroll finished from close range in the 52nd minute to break the deadlock before Craig Bellamy grabbed Liverpool’s second on 61 minutes.
Liverpool added a third when Dirk Kuyt, the goal hero in the Merseysiders 2-1 FA Cup win over Manchester United last weekend, rounded off a sweeping counter-attack 12 minutes from time.