Defeats by Tottenham Hotspur, Swansea and Sunderland had left United at risk of losing four successive games for the first time since 1961, but they blew off the cobwebs with an assured display at Old Trafford.
Antonio Valencia and Danny Welbeck claimed second-half goals to leave United four points outside the Premier League's top four in seventh place, six days after Swansea had dumped them out of the FA Cup on the same pitch.
Teenage winger Adnan Januzaj was the catalyst for United's victory and he went close to opening the scoring in the 11th minute with a free-kick that struck the crossbar.
Welbeck also squandered a glorious chance when he bundled wide, but the pressure told early in the second period when Valencia tapped home after Gerhard Tremmel parried a header from Shinji Kagawa.
Januzaj provided the cross for Kagawa and he was also the source of United's second goal, in the 59th minute, with a centre that was cleared to Patrice Evra, whose first-time shot was deftly flicked home by Welbeck.
Chris Smalling somehow contrived to volley over from a cross by Kagawa, who also had a shot blocked on the line.