A dour opening half came to life just before the break when the visitors scored twice in two minutes.
First, Henrikh Mkhitaryan latched onto Chris Smalling’s flick-on and raced through on goal before beating Kasper Schmeichel with a clinical finish.
Zlatan Ibrahimovic then took advantage of terrible Leicester marking to side-foot home his 15th Premier League goal of the season.
Juan Mata ensured there was no way back for the hosts when he finished off a one-two with Mkhitaryan early in the second half.
Leicester never looked like scoring, with their only shot on target a tame Wilfred Ndidi strike just before half-time.
Manchester United remain in the hunt for a top-four finish. They are sixth, one point behind Liverpool and two behind fourth-placed Arsenal.
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