Newcastle's Peter Lovenkrands became the first player to score past United keeper Edwin van der Sar in the league for more than 21 hours with a ninth-minute tap-in but Wayne Rooney levelled and Dimitar Berbatov sealed the points after the break.
United's 11th consecutive league victory took them to 65 points from 27 games. Chelsea and Liverpool, who have both played a game more, are both back on 58 with time running out.
Watch Premier League highlights now on the VPlayer
Fourth-placed Aston Villa's Champions League ambitions were dealt a blow with a 2-0 loss at Manchester City while Stoke City climbed out of the bottom three with a 2-0 home victory over Bolton Wanderers.
West Ham United won 1-0 at Wigan Athletic.
Tottenham Hotspur shook off the disappointment of losing to Manchester United in Sunday's League Cup final with a 4-0 hammering of Middlesbrough to ease their relegation worries.
Fifth-placed Everton drew 0-0 at Blackburn Rovers while Hull City scored late to beat Fulham 1-0 at Craven Cottage to halt their recent slide.
United, who are closing in on an 18th league title, saw their lead reduced by Chelsea and Liverpool on Tuesday and their rivals would have been hoping for a favour from a Newcastle side is desperate need of points.
They could not have been expecting Van der Sar to offer them a chink of light, but the veteran Dutchman did just that after nine minutes when he spilled a cross from Jonas Gutierrez and Dane Lovenkrands was on hand to punish the error.
"We got off to a terrible start and Newcastle were on top," United manager Alex Ferguson, who was clearly not happy with his side's early efforts, told Sky Sports.
"Edwin said himself he made a mess of it. It was a hairy spell for us. It was going to happen sometime," he added, referring to Van der Sar's rare slip.
United were at sixes and sevens early on and they were lucky to see Obafemi Martins shoot into the side-netting when he had a great chance to put Newcastle 2-0 ahead.
Normal service was resumed after 20 minutes when Rooney, who missed United's League Cup final success through illness, beat Steve Harper with a shot on the turn.
A niggly first half ended with Cristiano Ronaldo and Steven Taylor getting involved near the touchline and Rio Ferdinand receiving a yellow card.
Taylor was badly at fault for United's winner after 56 minutes when he attempted to chest the ball back to his keeper but instead gave the ball to Park Ji-sung who in turn fed Berbatov to score with ease.
"We required a lot of grit at times," said Ferguson. "Whenever you come back from 1-0 down to win you must be pleased."
Villa were looking for an eighth consecutive away league victory but were second best at Manchester City who won with goals from Elano and Shaun Wright-Ph
