Michael Carrick toe-poked United ahead with a scrappy goal after four minutes and Robin van Persie ended his 10-match scoring drought with a 66th-minute penalty to seal the points in a game United dominated from start to finish.
They now have 80 points from 32 games, 15 clear of current champions Manchester City, who have 65 with seven matches to play.
"It was an important win and we are one game closer to the title. The important thing is not to take our eye off the ball," United manager Sir Alex Ferguson told Sky Sports.
It was their biggest win over their arch-rivals at St James' Park since 1966 and their first there since 2000.
The win, their first for 10 league matches, came thanks to goals from Stephane Sessegnon, Adam Johnson and David Vaughan, and together with Stoke's defeat, lifted Sunderland into 15th place with 34 points.
The hosts' defence failed to clear a United corner and the ball bobbled around in front of goal before Carrick reacted to poke it past Stoke goalkeeper Asmir Begovic.
"It was a big win. It was important that we bounced back from last Monday," said Van Persie, after netting his 20th league goal of the season.
"My goal came at an important time, but I wouldn't have cared who scored the goal. Every single player battled out there and we deserved it."
Di Canio, who replaced Martin O'Neill and saw them beaten in his first match in charge at Chelsea last week, celebrate
