Victory, secured by two goals apiece from Nani and Wayne Rooney, saw the champions close to within two points of leaders Manchester City.
But City — also knocked out of the Champions League in midweek — will restore their five-point advantage at the top if they win away to Chelsea on Monday.
Nani gave United a 17th-minute lead at Old Trafford with a low shot from 20 yards out for his first goal in 18 games.
And 10 minutes later before Rooney’s shot through a crowd of players gave the England striker his first league goal in nine games.
Steven Fletcher pulled a goal back for Wolves early in the second half but United restored their two-goal lead after Nani turned in Antonio Valencia’s cross.
Valencia was also the provider when Rooney made it 4-1.
“I always say December is an important month; if we get to the new year still in the frame we have a great chance,” said United manager Sir Alex Ferguson.
Elsewhere, Arsenal marked their 125th anniversary with a 1-0 win at home to Everton thanks to a goal from in-form striker Robin van Persie.
The Dutch international broke the deadlock at the Emirates with a brilliant left foot volley 20 minutes from time.
“It’s an art Robin has mastered well,” said Arsenal manager Arsene Wenger. “We are also grateful for three points against a good Everton side.”
Liverpool beat QPR 1-0 at Anfield thanks to Luis Suarez’s first goal in six games with the Uruguayan heading home two minutes after half-time.
Norwich held off 10-man Newcastle to win 4-2 at Carrow Road.
Newcastle fell behind when, from a 39th-minute corner, a goalmouth scramble ended with Wes Hoolahan putting the Canaries ahead.
But Newcastle were level before half-time when striker Demba Ba ran on to Yohan Cabaye’s through ball for his 10th goal in as many league games.
Norwich, however, then scored two goals in four minutes with headers from Grant Holt and Steve Morison.
Newcastle, who had Dan Gosling red-carded, made it 3-2 when Ba scored his second but Holt calmed Norwich nerves when he headed in from 12 yards to make the score 4-2.
“You can’t concede from three set-plays in the Premier League like we did, but any team would struggle with the injuries we’ve got in central defence,” said Newcastle manager Alan Pardew.
“We’re still aiming for a top seven or eight finish if we can.”
Wigan climbed off the bottom with a come from behind 2-1 win over West Brom.
The Baggies went ahead at the Hawthorns when midfielder Steven Reid curled in a 22-yard free-kick.
But minutes later Victor Moses drew Wigan level with a curling strike from the edge of the box.
Wigan went ahead in the 57th minute when Jordi Gomez scored from the penalty spot after Reid fouled Moses.
“We showed great composure and I was extremely proud,” said Wigan manager Roberto Martinez.
Aston Villa took the lead away to struggling Bolton when the unmarked Marc Albrighton turned in a cross from Gabriel Agbonlahor 12 minutes before half-time and more poor defending gave Stiliyan Petrov room for a long-range shot that went in via a deflection off Gary Cahill.
Bolton hit through Ivan Klasnic scored in the 55th minute but they were unable to find another goal and Owen Coyle’s men are now propping up the table.
“We are left to rue one sloppy 10 minute period,” said Coyle.
Swansea defeated Fulham 2-0 with Scott Sinclair opening the scoring with a 56th-minute strike which was deflected into his own net by Clint Dempsey.
United States international Dempsey had the chance to equalise but his penalty was superbly saved by Michel Vorm.
Swansea substitute Danny Graham then sealed victory on the stroke of full-time.
Tottenham Hotspur, who started the weekend in third place, are away to Stoke on Sunday when Sunderland, in Martin O’Neill’s first game as their manager, face fellow drop candidates Blackburn Rovers.