The contest was over less than a minute into the second half, with Ibrahimovic opening the scoring on the half-hour mark before Sebastian Larsson was sent off for a strong challenge on Ander Herrera.
Mkhitaryan doubled United's advantage just 47 seconds after the break, and without a Sunderland player touching the ball. Marcus Rashford added a late third to end his long goal drought.
With the Premier League's top four all having won on Saturday, it was essential for United to return to winning ways having been left disappointed by home draws in its previous two games.
The result took Jose Mourinho's side above Arsenal into fifth and within four points of fourth-placed Manchester City, which has played one more game. Sunderland remains bottom, 10 points adrift of safety.
United laboured through a subdued opening 30 minutes before Ibrahimovic, as he has done many times this season, took matters into his own hands.
The Swedish forward demanded the ball be played to him on the edge of the penalty area, and then evaded the attempts of two Sunderland defenders to halt his progress before sending an unstoppable strike into the far bottom corner.
Sunderland spurned its best chance of the game ten minutes later when Victor Anichebe did his best Ibrahimovic impression, holding off Eric Bailly before forcing a fine save from stand-in United keeper Sergio Romero.
However, the home side's hopes of a revival were all but ended two minutes before the break when Larsson was sent off for a dangerous lunging challenge on Ander Herrera.
Less than a minute into the second half another moment of individual brilliance doubled United's lead.
Mkhitaryan received the ball just outside the penalty area on the left, before dribbling past two Sunderland defenders and finding the bottom corner with a left-foot drive across goal.
United had plenty of chances to extend its lead as Sunderland tried to get back in the game and finally took one in the 90th.
Paul Pogba rounded off a commanding performance by releasing Rashford into space down the right. The forward exchanged passes with Ibrahimovic before finishing powerfully across goal.
Unlike its rivals, United can still qualify for next season's Champions League by winning the Europa League. It resumes its campaign with a quarterfinal first leg in Belgium against Anderlecht on Thursday.