The Red Devils, who had lost their last two top-flight games heading into this one, put their opponents to the sword with four goals in the first half.
Defending champions Leicester did pull one back on a day to forget at the Theatre of Dreams, but United comfortably saw things through to make it back-to-back wins in all competitions after a testing week for Jose Mourinho.
The first half actually got off to a slow start, with neither side attempting a shot on target in the opening 20 minutes of the contest between these two heavyweight teams.
It was United, minus dropped skipper Wayne Rooney, who drew first blood a quarter of the way in when captain for the day Chris Smalling outjumped Robert Huth and got the beating of stand-in keeper Ron-Robert Zieler to head home the opener.
Leicester had enjoyed a decent spell of possession up until that key breakthrough goal, arguably getting the better of the midfield battle and creating some promising positions down either flank which they struggled to capitalise on.
It was a different story the moment Smalling's goal hit the net, though, as a breathtaking 20-minute spell saw three more goals arrive for Mourinho's men.
Marcus Rashford and Zlatan Ibrahimovic had both missed good chances to add a second, the latter coming close to scoring a Goal of the Season contender with his half-volley on the swivel, while Paul Pogba's 30-yard strike was turned aside by Zieler.
United then stepped things up a level, scoring at the end of an 18-pass move when Pogba's latest scooped pass was flicked into the path of Juan Mata by Jesse Lingard for the Spaniard to blast into the corner.
A short corner led to the third of the match, with Mata driving into the box and blasting across goal for Rashford to continue his impressive scoring run, before another well-worked corner led to Pogba glancing home his first for the Red Devils since returning to the club in the summer.
With the game as good as up by the midway point, Claudio Ranieri - who had not lost any of his most recent four games against Mourinho - took off his two star men as Jamie Vardy and Riyad Mahrez made way.
That decision was perhaps taken with one eye on the Champions League tie with Porto in three days' time, but despite damage limitation being on the mind Leicester did have a goal back on the hour.
Following slow start to the half for both sides, Gray cut inside from the left and picked out the top corner with the best goal of the game to give his side the faintest of hopes.
United were not willing to let their opponents back into the game, though, as both Ibrahimovic and Lingard came close to regaining the four-goal margin when sending their shots narrowly off target.
Leicester, now with just one win in their last 17 meetings against the Red Devils, had chances of their own to make things a little more interesting - King holding his run but sending his shot straight down the throat of David de Gea.
Gray had another attempt turned over the bar by De Gea inside the closing 10 minutes, but United held on to ensure that Mourinho avoided three defeats on the spin in league competition as his side climbed up to third place ahead of a busy afternoon programme in the top flight.
Leicester, meanwhile, are stuck in the bottom half after a third away defeat on the spin - the first time that has happened since December 2014 - and have already equalled their tally of losses from last season's title-winning campaign.