Quickfire goals either side of half time from Henrikh Mkhitaryan, Zlatan Ibrahimovic and Juan Mata ensured that the visitors ended a run of three consecutive draws in the Premier League, leaving Leicester just one point clear of the relegation zone.
United were able to make the most of defeats for Arsenal and Liverpool yesterday, but the game got off to a slow start and Marcos Rojo's half-volley which drew a routine stop from Kasper Schmeichel was the closest either side came in the opening 20 minutes.
The uneventful and uninspiring start to the match convinced United manager Jose Mourinho to slightly alter his system after 20 minutes, and that allowed the visitors to gain an element of control over proceedings.
The first clear chance of the game arrived shortly afterwards when Mkhitaryan delivered a cross from the right following a sweeping team move, but Marcus Rashford could not keep his half-volley down having found space inside the area.
Rashford threatened again with 10 minutes left of the first half when Ibrahimovic and Paul Pogba combined to find the youngster, but this time Schmeichel reacted quickly to make a smart save down low to his right, keeping out the drive at his near post.
Having held their own for the majority of the first half, though, Leicester saw the game slip away from them courtesy of two goals in the space of just 88 seconds shortly before the break as United suddenly sparked into life.
It was Mkhitaryan who provided the piece of quality the game had been lacking up to that point in order to break the deadlock, beating Robert Huth to the ball just inside the Leicester half before racing through on goal and firing past Schmeichel.
One quickly became two as United took control of the game from nowhere, with Ibrahimovic scoring his 20th of the season when he swept a low Antonio Valencia cross through the legs of Wes Morgan and past a helpless Schmeichel - a goal which saw the Swede become the oldest player to score 15 times in a single Premier League campaign.
United scored three times in the space of seven minutes on their way to a 4-1 win over Leicester in the reverse fixture, and they repeated that feat either side of half time as they picked up where they left off upon the restart.
It took just four minutes for the visitors to add their third of the afternoon as Mata played a one-two with Mkhitaryan before sweeping the ball past the keeper at his near post having been left by Christian Fuchs and played onside by Morgan.
United could have had a fourth just three minutes later as Leicester continued to collapse, with Rashford racing onto a through-ball before seeing his low drive across goal turned behind by Schmeichel.
The Foxes came up with a rare attacking moment of their own shortly before the hour mark when Riyad Mahrez rippled the side-netting with a free kick, but United were soon back on the front foot and Mata should have doubled his personal tally when he beat the offside trap only to lift a tame finish into the arms of the keeper.
United's blitz either side of half time meant that they were able to play the rest of the match almost at walking pace as they knocked the ball around comfortably, and they nearly added a fourth with seven minutes remaining when Mkhitaryan fired over from just inside the area.
Leicester avoided any further damage, but still became the first top-flight champions to fall to four consecutive league defeats since Liverpool in 1982-83, while they are now the first side in Premier League history to have failed to score in their opening five matches of a calendar year.
It is also the first time the Foxes have fallen to consecutive home league defeats for two years, leaving them just one point clear of the relegation zone and only two off bottom following wins for Sunderland and Hull City yesterday.
United, meanwhile, extend their unbeaten run to 15 matches - the best current streak of any team in Europe's top five leagues - to move within two points of the Champions League places and only one behind fifth-placed Liverpool.