Zlatan Ibrahimovic put United 1-0 up on 30 minutes with a fine turn and low shot on the edge of the box, before Larsson was harshly sent off by Craig Pawson for a high tackle on Ander Herrera.
Just 45 seconds after the restart, United were 2-0 up through Henrikh Mkhitaryan, who found the bottom left corner from 15 yards with his left foot as Sunderland stood off.
Substitute Marcus Rashford added a third with a minute remaining, finishing well into the bottom corner from inside the area after Ibrahimovic’s assist.
The result means Sunderland remain bottom of the Premier League, 10 points from safety with seven games remaining, while United are up to fifth, four points off fourth-place Man City but with a game in hand.
Jose Mourinho made five changes from midweek, starting Luke Shaw following criticism over the past week. Sergio Romero came in for the injured David de Gea, while Marouane Fellaini was named captain.
Sunderland made just one change, with Victor Anichebe replacing Fabio Borini.
The first real chance of the game fell to Jesse Lingard, who was awarded with a new contract in midweek, but the Englishman’s low effort from the edge of the box was tipped wide by Jordan Pickford.
But Pickford could do nothing about the opening goal a minute later when Ibrahimovic’s turn and shot from nothing 18 yards out curled into the bottom right-hand corner.
Ibrahimovic has now scored 250 goals in 308 appearances since he turned 30 in 2011, having scored 232 before his 30th birthday.
Sunderland were nearly level five minutes before the break through Anichebe, but Romero rushed out well to block the striker, who could argue that Eric Bailly’s trailing foot shoved him off balance.
The hosts were reduced to 10 men just two minutes before the break when Larsson’s slightly high foot went through Herrera; referee Pawson did not hesitate in pulling out the red card when a yellow arguably seemed more appropriate.
After the break, United were ahead before Sunderland had managed to touch the ball as Mkhitaryan struck well into the bottom corner, but the Armenian had Lamine Kone to thank for standing off him inside the area.
Chances were at a premium after the second goal, though Ibrahimovic did go close to adding a second with a deflected cross-shot, which Pickford reacted well to.
Paul Pogba wildly volleyed over the bar from Ibrahimovic’s cut-back, before Jermain Defoe fired just over the bar with a well-struck effort from the edge of the box at the other end.
Rashford wrapped up the points in the 89th minute, finishing into the bottom left corner from 10 yards out after man-of-the-match Ibrahimovic had teed him up.
It ended 3-0, meaning United are still in the hunt for a top four Premier League spot, while Sunderland have now gone 675 minutes without a goal in the top flight.