Anthony Martial and Marcus Rashford were on target as a Paul Pogba-less United eased past a lacklustre Burnley side to close in on the top four in the standings.
United have now taken 13 points from their last six games. Frenchman Martial scored his 10th goal of the season from close range after his brace against Newcastle United on Boxing Day.
Andreas Pereira set him up after he robbed Charlie Taylor and crossed superbly from the right. Rashford then raced clear in stoppage time to seal the victory.
Meanwhile, Leicester City beat West Ham 2-1 which saw the latter's manager Manuel Pellegrini being sacked as the club succumbed to their ninth loss in the past 12 matches. Second-placed Leicester rode goals from Kelechi Iheanacho and Demarai Gray to win the tie. For West Ham, Pablo Fornals found the back of the net. Everton, meanwhile, had striker Dominic Calvert-Lewin to thank as he scored twice to give the side a 2-1 win at Newcastle United.
It was a second consecutive win for Everton's new manager Carlo Ancelotti, who made his debut at Goodison Park with a 1-0 win over Burnley on Thursday.
Southampton rode Danny Ings' goal to grab a point against Crystal Palace with a 1-1 draw at St. Mary's Stadium. James Tomkins had given Palace the lead.
Ten-man Watford, elsewhere, dominated Aston Villa with a 3-0 win. Troy Deeney netted a brace as they played with 10 men for more than half an hour.
( With inputs from IANS )