Marcus Rashford gave the Red Devils the lead in the first half with a calm finish past Kasper Schmeichel. United's lead didn't last long though.
Bruno Fernandes was caught dwelling on the ball in midfield by Wilfred Ndidi, before the ball eventually found its way through to Harvey Barnes who lashed a left-footed shot past David De Gea from outside the box.
Fernandes got his goal in the 79th minute though, after he was played through on goal by a beautiful pass from Edinson Cavani.
Once again, though, they didn't keep their lead for long, as an Axel Tuanzebe own goal meant that the points were shared. Ayoze Perez played a nice cut-back from the by-line, and Jamie Vardy's shot trickled in off the young defender, who could do little about it.
Here's how each player fared in the game.
Leicester City Player Ratings
Kasper Schmeichel - 7/10
The Leicester captain made a stunning save in the second half to deny Rashford from point-blank range. There was little he could've done about either goal, though.
James Justin - 6/10
Justin defended well for most of the game. However, he blew a few crossing opportunities when he got into good positions. Shaw defended well against both him and Albrighton.
Wesley Fofana - 7/10
Fofana was once again superb at the heart of the Leicester defence. He defended magnificently to stop Daniel James from putting Fernandes through on a counter-attack, in a move that really should have ended with United scoring.
Jonny Evans - 5/10
For both the Manchester United goals, Evans was the man to play the attackers onside. He also got caught once too often in possession, which put Leicester under pressure.
Timothy Castagne - 6/10
The left flank was certainly the one that was bringing Leicester more joy when they attacked. Castagne was the perfect foil for Barnes, as he was steady when the ball broke on that flank.
Wilfred Ndidi - 6/10
Ndidi had an effective game in midfield for most of the time against Fernandes. It was also his tackle on the Portuguese that won the ball for Leicester for Barnes to score their first equaliser.
Youri Tielemans - 7/10
That Leicester controlled possession for large periods of the game was down to Tielemans's composure and quality on the ball. He had a chance to win them the game in stoppage time, but lashed at a left-footed shot from outside the area.
Marc Albrighton - 4/10
Albrighton had a poor game. He did provide cover for Justin on the defensive side, but his quality with his crossing was non-existent.
James Maddison - 4/10
Like Albrighton, Maddison's quality deserted him on the day as well. He could've made amends with a free-kick in the second half, but couldn't get it past Rashford in the wall.
Harvey Barnes - 8/10
Barnes was superb on the left flank. He ran at Victor Lindelof when he had the chance, and was a menace. He capped his day off with a sensational goal from outside the box as well.
Jamie Vardy - 6/10
Vardy worked hard and tried to get into positions to threaten United, but Leicester didn't get the ball to him enough. He will also be miffed that the second equaliser was registered as a Tuanzebe own-goal. It was great movement from him though, as he stood still in the box to receive the cut-back from Perez.
Ayoze Perez - 7/10
Perez made a big impact after coming on to replace Albrighton. He played the telling pass for the second equaliser, and looked a lot more threatening than Albrighton did at any point of the game.