The champions, without injured striker Wayne Rooney, laboured at Molineux but Scholes pounced for his 100th league goal after 73 minutes to put United on 63 points, two ahead of Chelsea who are in FA Cup action against Stoke City on Sunday.
Arsenal also turned up the heat on Chelsea, beating Burnley 3-1 at the Emirates to move level on 61 points with Carlo Ancelotti's side. But for wayward finishing by Nicklas Bendtner the Gunners would have gone second on goal difference.
Wolves, at full-strength after being fined 25,000 pounds for fielding a weakened side at Old Trafford earlier in the season, poured forward in the first half and could have gone in front when Stephen Ward failed to convert a close-range header.
United perked up in the second period and Scholes scored with a right-foot shot from eight metres after defender Jody Craddock slipped as he stretched to block.
Wolves should have equalised in stoppage time but the unmarked Sam Vokes fired wildly over from six metres.
"We deserved the win, no question," United manager Alex Ferguson told ESPN television. "They had an outstanding chance at the end but the lad didn't take it.
"Our form is good and we're managing without some players, which is important at this time of year."
Ferguson was also pleased to see Wes Brown, Nemanja Vidic, Rio Ferdinand and Patrice Evra reunited in defence.
"That was the first time that back four has played together for a year and a half," he said.
ARSENAL WIN
At Arsenal, goals by Cesc Fabregas, Theo Walcott and Andrei Arshavin left Burnley mired in the relegation zone having managed just one point on the road this season.
It was the eye-of-a-needle passing of Fabregas and Samir Nasri that opened the massed Burnley ranks and enabled the Spaniard to cleverly tuck in the opener after 34 minutes.
Fabregas limped off a few minutes later with a hamstring strain and manager Arsene Wenger said he would not know until Sunday whether it would rule the midfielder out of Tuesday's Champions League game against Porto.
Arsenal paid for their profligacy when David Nugent was given space to run through the middle and lift the ball over keeper Manuel Almunia five minutes into the second half.
Walcott restored the lead 10 minutes later with a well-taken curling shot but while the fans sat back to await a goal rush, the misses left them nervous before Arshavin finally killed it off in stoppage time.
With an easier-looking run-in than either of their two rivals, Arsenal remain in the hunt for their first title success since 2004.
"We have a great togetherness, that is for sure. When you have gone through what we have this season and stand where we are you have to be mentally strong," manager Arsene Wenger told Sky Sports News.
"Everybody buried us 10 times and we are still there. We have belief and hunger so we will fight."
