With United not playing Tottenham until tomorrow, City, who gave a full debut to new 27million striker Edin Dzeko, knew they would move a point ahead of their local rivals - albeit having played three games more - with victory today.
But it was Wolves who took a 12th-minute lead as Nenad Milijas drew a fine save from Joe Hart, then followed up his own effort to stab home the rebound.
Mick McCarthy's side had chances to score a second but City held firm and ensured they would be level at half-time when centre-back Kolo Toure rifled in a shot from a corner in the 40th minute.
The points seemed to have been wrapped up by the hosts in the opening nine minutes of the second half when first Carlos Tevez (49) finished off a brilliant run with their second and then Yaya Toure combined with Tevez and Dzeko for his fourth of the season.
In the 66th minute Tevez headed in City's fourth, but Wolves were not finished and Kevin Doyle converted a penalty two minutes later before Ronald Zubar made it 4-3 four minutes from time when his header was adjudged to have crossed the line.
The visitors poured forward in search of an unlikely equaliser but City held on through five minutes of stoppage time.
Chelsea secured only their second win in their last 10 league games with goals from Branislav Ivanovic and Nicolas Anelka in a 2-0 victory over Blackburn at Stamford Bridge.
Ramires and Anelka both hit the woodwork in the first half but they did not make the breakthrough until defender Ivanovic lashed home following a corner in the 57th minute, with Anelka making the points safe 14 minutes from time.
West Brom ended a run of six successive defeats with a 3-2 victory over Blackpool in a topsy-turvy clash at The Hawthorns.
Ian Holloway's side went ahead in the 11th minute through a brilliant chip from David Vaughan before Peter Odemwingie beat the offside trap in the 37th minute and coolly slotted home his seventh of the season to level.
James Morrison then put the hosts ahead in the 52nd minute and Odemwingie, who had not scored since December 5, grabbed the winner three minutes from time after Gary Taylor-Fletcher had equalised for Blackpool in the 80th minute.
Bolton suffered their fifth consecutive away defeat as Stoke secured a 2-0 victory at the Britannia Stadium to move level on 30 points with their opponents.
Danny Higginbotham's scrappy goal broke the deadlock in the 37th minute and Matthew Etherington made the points safe from the penalty spot 63 minutes in after he had been brought down by Zat Knight, although Jussi Jaaskelainen maybe should have saved it.
Draw specialists Fulham had to settle for a point again in a 1-1 draw with Wigan, but it was Mark Hughes' side who were the happier after Andrew Johnson's 86th-minute goal.
It was the injury-troubled striker's first Premier League strike since March 2009 and cancelled out Hugo Rodallega's 57th-minute opener for the Latics.
The Colombian twice hit the woodwork as Wigan sought a valuable three points, while Fulham had a goal chalked off after Clint Dempsey was ruled to have handled the ball.
What is reportedly set to be Avram Grant's last match as West Ham boss ended in a 3-0 defeat tonight at the hands of Arsenal, who moved to within two points of City.
Robin Van Persie put the Gunners ahead in the 13th minute from Theo Walcott's cross, and the roles were reversed four minutes before the break when Hammers debutant Wayne Bridge got in a muddle and Van Persie set up Walcott for the second.
Bridge's miserable afternoon was complete in the 77th minute when he brought down Walcott in the area and Van Persie made no mistake from the spot.