Ryan Giggs also struck for the champions who now have 31 points from 14 games, two behind Chelsea who play at third-placed Arsenal (25 points) on Sunday.
Tottenham Hotspur drew 1-1 with Aston Villa at Villa Park in the late game to leapfrog Arsenal and go third in the standings on 26 points, while Manchester City remain sixth on 22 after they were held 1-1 at home by struggling Hull City to record a Premier League record seventh successive draw.
West Ham United beat Burnley 5-3 while Wigan Athletic bounced back from last week's 9-1 hammering at Spurs by beating Sunderland 1-0.
The referee evened things up seven minutes later with another hotly debated penalty award when he decided Frederic Piquionne had had his shirt pulled and Kevin Prince Boateng scored from the spot.
SOFT GOALS
"It was a strange game because if you analyse it you can say it was a good game for us. We created a lot of chances and conceded soft goals," Grant told Sky Sports.
United's ability to win comfortably without hitting top form is in marked contrast with cross-town rivals City, whose top-four aspirations recede with every passing stalemate.
"Today I sensed a little bit of anxiety in our play. We've been in this situation of giving away a winning position. On the day a draw was probably all we could ask for," City manager Mark Hughes said.
Villa went ahead after 10 minutes courtesy of Gabriel Agbonlahor's close-range strike, though the home side lived dangerously at times and Spurs deservedly equalised with a thumping drive by defender Michael Dawson after 77 minutes.
