David Moyes' former club got the job done against the reigning champions to break a 21-year drought at the Theatre of Dreams and secure their spot in the Premier League's top five.
Bryan Oviedo, deputising for Leighton Baines at left-back, scored his second goal in two outings when he arrived unmarked at the back post to slot home Romelu Lukaku's cross with just four minutes of regular time remaining.
The defeat condemned United to ninth place on the league table, some 12 points off league leaders Arsenal, while the fifth-placed Toffees stretched their unbeaten run to seven matches by winning at Old Trafford for the first time since 1992.
2013/14 Premier League scores
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