The Foxes were flying out of the blocks in the opening exchanges and took just 10 minutes to take the lead, with Youri Tielemans picking out young Luke Thomas at the far post as the left-back's volley sailed past a hapless David de Gea.
Leicester had United pinned back in their own half as the second period got underway and they got their reward with 66 minutes on the clock, as Caglar Soyuncu powered a header home from Marc Albrighton's corner, and a late period of United pressure failed to bear fruit.
Man City now boast an unassailable 10-point lead over Man United with three games left to play, while Leicester have leapfrogged Chelsea back into third place as the race for Champions League football hots up.
United now have another 48 hours to recover before they welcome Liverpool to Old Trafford on Thursday, while Leicester have the small matter of an FA Cup final with Chelsea on Saturday.
10th min: Leicester draw first blood. Youri Tielemans finds himself in plenty of space down the right and picks out Luke Thomas at the far post, and the left-back powers a sumptuous volley into the top corner. 0-1.
Pick that one out! 🚀🎯— Football on BT Sport (@btsportfootball) May 11, 2021
Luke Thomas with an inch-perfect strike into the top corner to give Leicester the lead!
His first Premier League goal too! pic.twitter.com/CJ8q0PgKqJ
14th min: United's first attack of the game ends in an equaliser. Amad Diallo out-muscles Thomas and picks out Mason Greenwood, who skips away from Caglar Soyuncu to fire home into the far corner. VAR checks it for a possible handball but the goal stands. 1-1.
28th min: De Gea is forced to tip Tielemans's dangerous cross over the bar for a Leicester corner, but United manage to clear.
45 +1 min: Leicester free kick in a promising position as Diallo brings down Wilfred Ndidi. Tielemans takes but it hits the wall as the half-time whistle blows.
46th min: Kelechi Iheanacho has an early opportunity in the second half which is blocked, and the resulting corner comes to nothing.
51st min: Iheanacho goes for the spectacular, but his curling effort is high and wide.
59th min: Tielemans picks out Iheanacho, who only has De Gea to beat from a narrow angle, but the Spaniard covers his near post well and saves.
66th min: Albrighton finally gets a corner right and Leicester take advantage. The Englishman floats in a ball towards the far post, and Caglar Soyuncu towers above Nemanja Matic to power a header home. 1-2.
Caglar Soyuncu with a thunderous header! 💥— Football on BT Sport (@btsportfootball) May 11, 2021
There was no stopping him there!
Leicester regain their lead against Man Utd 🦊 pic.twitter.com/Pcdrpp93hZ
73rd min: Iheanacho's cross finds Vardy at the back post, and the striker heads it towards Tielemans in acres of space at the back post, but the midfielder just cannot poke it home.
78th min: James Maddison cuts inside and gets a shot away on his right foot which curls wide of De Gea's goal.
84th min: A swift United move ends with Bruno Fernandes lining up a half-volley, but the Portuguese playmaker slices it well wide of the Leicester goal.
MAN OF THE MATCH - YOURI TIELEMANS
As he does week in week out, Youri Tielemans pulled the strings in the Leicester midfield, and he once again formed an excellent partnership with Ndidi for the 90 minutes at Old Trafford.
The Belgian midfielder claimed a terrific assist for Thomas's opener and so nearly added to his goals tally in the second half, but it was an all-round confident showing from Tielemans, who played his part defensively as well.
It is never easy for any teenager to come to Old Trafford and set the world alight, but 19-year-old Luke Thomas surely could not have dreamed of a better place and better way to score his first Premier League goal.
The defender volleyed home with the panache of an experienced centre-forward and thoroughly deserved to be on the winning side at Old Trafford.
2006 - Amad Diallo Traore assisting Mason Greenwood is the first time two teenagers have combined for a Premier League goal since May 2006, when David Wheater set up Adam Johnson for Middlesbrough against Bolton. Dirtbags. #MUNLEI— OptaJoe (@OptaJoe) May 11, 2021
Possession: Man United 53%-47% Leicester
Shots: Man United 4-12 Leicester
Shots on target: Man United 1-3 Leicester
Corners: Man United 3-4 Leicester
Fouls: Man United 9-12 Leicester
MANCHESTER UNITED (4-2-3-1): De Gea; Williams, Tuanzebe, Bailly, Telles; Matic, Van de Beek; Diallo (Fernandes 78'), Mata, Elanga (Rashford 65'); Greenwood (Cavani 65')
LEICESTER CITY (3-4-1-2): Schmeichel; Castagne, Fofana, Soyuncu; Albrighton, Ndidi, Tielemans, Thomas; Perez (Maddison 65'); Iheanacho, Vardy (Choudhury 80')