The game took a while to get going but three goals in a seven-minute spell either side of half-time ended the game as a contest as Jose Mourinho's men got a crucial win.
Henrikh Mkhitaryan scored a wonderful opening goal before Zlatan Ibrahimovic added a second just before half time.
Juan Mata then rounded off the scoring four minutes into the second half to give United a vital three points, while the Foxes sit just one point off the bottom three after this result.
Rooney missed the game due to illness
The big news before the game for United was the fact that Wayne Rooney was not in the squad due to illness with Mata coming into the starting lineup as his replacement.
Sloppy first half hour from both teams
Mourinho deployed a 4-4-2 formation from the start, though that only lasted for 20 minutes as the visitors just couldn't get going. After Mourinho's change from a two-striker system, United began to dominate proceedings.
United should have gone in front when a fast-flowing move ended with a cross from Mkhitaryan finding Marcus Rashford in the box but the striker put his shot well over the bar when he should have hit the target.
Rashford had yet another chance not long after his first as his low driven shot from the edge of the box was well saved by Kasper Schmeichel, who had to get down well to his right to keep it out.
Two goals in two minutes put United in firm control
United's dominance in the last part of the first half finally did tell though as they scored two goals in two minutes before the half-time whistle.
The first goal was scored by Mkhitaryan as he picked the ball up a long way out and managed to run right through the hosts' defence before calmly putting the ball into the back of the next past the helpless Schmeichel.
United made it two not long after the first when a lovely flowing move from the team ended with Antonio Valencia playing the ball to Ibrahimovic in the box and the striker hit it first time into the back of the net to score his 20th goal of the season.
Therefore, at half-time, the hosts were left shell-shocked after conceding two goals in a matter of minutes after being quite solid for most of the half and would need to improve in the second half.
Mata added a third goal just after half-time
The problem the hosts had, though, was that United made it three four minutes into the second half.
The goal once again came from a wonderful passing move which ended with a brilliant one-two from Mata and Mkhitaryan which Mata calmly stroked the ball into the net to end the contest with over 40 minutes to play in the game.
It should have been more shortly after when a long through ball from Paul Pogba found Mata one on one with Schmeichel but this time, the keeper stood up to make the save.
United players kept the ball well to see the game out comfortably
After that chance, United started to manage the game the way that Mourinho would have wanted them too by keeping the ball and making Leicester even more tired that they were during the game.
It worked a treat as the hosts barely troubled David de Gea in the second half and just before the end Pogba forced Schmeichel into a very good save from outside the box.
But overall, it turned out to a be a very comfortable win for United after they got the breakthrough and now they have moved within two points of a top four place while the hosts sit one point outside the bottom three.