Robin van Persie opened the scoring midway through the first half, latching on to Daley Blind’s chipped pass to fire past Mark Schwarzer.
There was a suspicion of offside as the striker darted beyond the defence, but referee Martin Atkinson denied Leicester’s appeals.
Moments later it was 2-0 as Van Persie sparked a quick counter-attack. The Dutchman’s pass released Angel Di Maria down the left and, despite Schwarzer saving the winger’s low drive, Radamel Falcao was on hand to slide home the rebound for his fourth United goal.
Louis van Gaal’s side were bursting with confidence and a minute before half-time they made it 3-0. Wayne Rooney’s whipped corner was flicked on by Blind and the unfortunate Wes Morgan diverted the ball into his own net for the second time this season.
Leicester offered little threat in the first half but pulled a goal back with 10 minutes of the match remaining through defender Marcin Wasilewski.
After the visitors’ set-piece appeared to break down, second-half substitutes Esteban Cambiasso and Marc Albrighton combined down the right and the former Aston Villa winger crossed for Wasilewski to head past David de Gea.
Albrighton volleyed a dipping drive narrowly over the bar a minute later before Di Maria raced up the other end and blasted his shot high above the Leicester goal.
It was a difficult afternoon for new Leicester signing Andrej Kramaric on his full debut, with the striker losing the ball for Blind to find Van Persie in the build-up to United’s opening goal.
The Croatia striker was replaced by David Nugent in the second half and the substitute tested De Gea from a tight angle after racing clear of the United defence.
The hosts looked to extend their lead in the closing stages but James Wilson, who had been sent on for Falcao, saw his shot saved by Schwarzer before Blind scooped the ball into the goalkeeper’s hands from the resulting corner.
United’s victory leaves them three points above fifth-placed Tottenham, while Leicester remain three points from safety at the bottom of the table.
Soccer Saturday reaction – Paul Merson
“United started very, very well and pressed from the word go. They played a real high tempo. They didn’t have a lot of shots, but they let Leicester know they were in a game. 3-0 at half-time, three shots, three goals. Against bigger and better teams later on in the season, and the way they played with the diamond – Januzaj, Mata and then Rooney – against top teams, that will have to be changed. I don’t make them a foregone conclusion [for a Champions League place].
“Leicester could look back at this in three months and think, ‘that second half was massive’. You get back in the dressing room and you say, ‘right, we won the second half. Now we’ve got to go into a home game.’ For me, it’s a must, must win [against Crystal Palace]. If they don’t win that, I just think it’s turn the floodlights off.”
Manchester United: De Gea (6), Valencia (6), Jones (6), Rojo (7), Shaw (6), Blind (8), Januzaj (7), Di Maria (7), Rooney (7), Van Persie (8), Falcao (7).
Used subs: McNair (6), Mata (6), Wilson (6).
Leicester City: Schwarzer (5), Simpson (6), Wasilewski (5), Morgan (5), De Laet (5), Drinkwater (5), King (6), Vardy (5), Kramaric (5), Schlupp (5), Ulloa (5).
Used subs: Cambiasso (6), Nugent (6), Albrighton (7).
Man of the match: Daley Blind