Much of the game's build-up had been dominated by a planned protest against David Moyes' management of the struggling champions, with a plane trailing the message 'Wrong One - Moyes Out' flown above Old Trafford during the contest.
A midweek defeat to local rivals Manchester City was the latest of United's setbacks in a tough season, tipping some fans over the edge.
And the turbulent atmosphere around the champions was heightened further as Ashley Westwood's second goal of the season gave Paul Lambert's side a shock lead.
However, Wayne Rooney - so often the bright light in United's faltering campaign - dragged the hosts in front with a double before half-time, taking his tally to six goals from his last six league games.
Any home jitters were put to rest 12 minutes into the second half as Juan Mata scored his first United goal, with the home fans responding with rousing renditions of pro-Moyes chants, before substitute Javier Hernandez rounded matters off late on with a typical poacher's finish after good work from Adnan Januzaj.
The win keeps United within reach of the top six and also serves as a perfect tonic ahead of Tuesday's UEFA Champions League quarter-final first leg against holders Bayern Munich.
Moyes was warmly applauded onto the pitch by the Old Trafford faithful, as those inside the stadium aired their backing of the manager, and the planned fly-over passed with little incident two minutes into the game.
However, the home fans' patience was put under strain 12 minutes in as Westwood curled a superb free-kick home and past David de Gea's despairing dive.
Villa kept the pressure on as Ciaran Clark sent a free header over the crossbar.
But United equalised on the counter-attack, a totally unmarked Rooney nodding Shinji Kagawa's cross past Brad Guzan.
That goal kicked United into gear, and they went ahead just before the interval as Leandro Bacuna's clumsy lunge on Mata resulted in a penalty that Rooney lashed past Guzan.
Christian Benteke wasted two big chances to equalise for Villa in the opening minutes of the second half and those misses came back to haunt the Belgian as Mata gave United breathing space.
Marouane Fellaini's presence in the penalty area played havoc for the Villa defence, and Mata stole in to open his United account with a low right-footed effort.
Rooney went close to a hat-trick, working space with a sensational first touch from a long ball only for Guzan to deny him, with the striker withdrawn soon after as Moyes turned focus to Tuesday's clash with Bayern.
Hernandez then got on the end of Januzaj's excellent cross in stoppage time to seal the impressive win and give Moyes renewed vigour ahead of arguably his toughest test since taking over from Alex Ferguson.
