In a tight contest that lacked real quality from both teams, Bruno Fernandes gave the Red Devils the lead with a 70th-minute penalty, but the Blues salvaged a point courtesy of a brilliant volley from Moises Caicedo just four minutes later.
Here, Sports Mole provides player ratings from Man United's stalemate with Chelsea.
Man United player ratings vs. Chelsea: Fernandes on target as Garnacho lacks cutting edge
GOALKEEPER
Amadou Onana - 6/10
Onana nearly gifted Chelsea an early goal with an sloppy hospital pass to Casemiro inside his own area. He was rarely tested after that until conceding the equaliser at his near post.
DEFENCE
Diogo Dalot - 6/10
Dalot was guilty of a rash challenge on Pedro Neto towards the end of the first half and was deservedly booked, but he dealt with his Portuguese compatriot reasonably well in the second half.
Matthijs de Ligt - 6/10
De Ligt stood firm to block a shot from Palmer inside the area in the first half. Dealt well with the threat of Jackson, but his performance was nothing spectacular.
Lisandro Martinez - 6/10
Martinez reverted back to central defence after a couple of games at left-back. Commanded the backline well alongside De Ligt, but was somewhat fortunate not to be sent off for a stud-showing tackle on the knee of Palmer at the end of the second half.
Noussair Mazraoui - 7/10
Mazraoui won more duels (eight) and completed more take-ons (four) than any other player between both teams in the first half, while he also won 100% of his duels and completed 100% of his take-ons. Impressed on his return at left-back.
MIDFIELD
Manuel Ugarte - 5/10
Ugarte is yet to justify his hefty £50m price tag since joining from PSG in the summer. The Uruguayan was bossed by Chelsea's midfield duo Caicedo and Lavia for most of the match and was at times untidy with the ball at his feet. He was also booked in the first half for a cynical foul on Palmer.
Casemiro - 6/10
Casemiro's severe lack of pace and mobility remains an issue for Man United and that was shown when Palmer breezed past him midway through the first half. The Brazilian did, however, contribute with a few crucial tackles and interceptions in the middle of the pitch.
Bruno Fernandes - 7/10
Fernandes lost the midfield battle with Caicedo, but he grew into the game in the second half, sprayed about some smart passes in the final third and confidently converted his penalty kick to give the Red Devils the lead.
ATTACK
Alejandro Garnacho - 4/10
It was an afternoon to forget for Garnacho, who looked a shadow of the player who excelled against Brentford last month. The winger struggled to get the better of both Malo Gusto and Reece James while he was frustratingly wasteful in the final third, most notably scuffing a glorious chance presented to him on a plate inside the penalty area by Fernandes in the second half.
Rasmus Hojlund - 5/10
Aside from showing his intelligence to win the penalty against Sanchez in the second half, Hojlund struggled to make his mark in the final third and failed to register a single touch in Chelsea's box during the first half.
Marcus Rashford - 6/10
Rashford sliced a side-footed shot against the woodwork at the end of the first half and looked lively a couple of times bursting down the left past Gusto, but it was a largely frustrating afternoon for the Englishan, who was booked for dissent midway through the second half and taken off in the 73rd minute.
SUBSTITUTES
Amad Diallo - 5/10
Came on in the 73rd minute and failed to make the desired impact in the final third.
Joshua Zirkzee - N/A
Came on in the 83rd minute and almost latched onto a cross at the near post in the closing stages.
Victor Lindelof - N/A
Replaced Ugarte in the 83rd minute and played the closing stages in midfield alongside Casemiro.
Chelsea player ratings vs. Man United: Caicedo caps superb display with sweet equaliser
GOALKEEPER
Robert Sanchez - 5/10
Sanchez had a quiet afternoon between the sticks, until he made the rash decision to clip Hojlund's ankle and concede a penalty, before being sent the wrong way from the resulting spot kick.
DEFENCE
Malo Gusto - 6/10
Gusto made several aggressive runs forward down the right and joined in with Chelsea's attacks, but he was never really in a position to provide a killer pass to one of the forwards. The Frenchman was booked towards the end of the first half for a late challenge on Ugarte and was then taken off at half time.
Wesley Fofana - 6/10
Fofana was involved in regular battles with Hojlund and came out second best on some occasions. He was thankful for James providing defensive cover throughout the match.
Levi Colwill - 6/10
Colwill got the better of Hojlund more often that not and was a commanding presence in the heart of the Chelsea defence, but he was careless with the ball at his feet at times and notably scuffed the ball out of play without any pressure around him early in the second half.
Reece James - 6/10
While Gusto burst forward on numerous occasions down the right, James rarely got forward as a left-back in the first half and instead sat back to provide support for centre-back pairing Fofana and Colwill. James was then moved over to right-back for the second half following Gusto's withdrawal, but he was unable to contribute from an attacking sense down the right.
MIDFIELD
Moises Caicedo - 8/10
The best player on the pitch. Caicedo's impressive all-round display, during which he made three tackles, three interceptions, three ball recoveries, two clearances and completed 86% of his passes, was capped by his brilliant volley struck low into the bottom corner.
Romeo Lavia - 6/10
Lavia was once again prefered in centre-midfield ahead of Fernandez, but there was nothing spectacular about his display. Some tidy passes and some wayward ones, too, before he was taken off 20 minutes from time.
Cole Palmer - 6/10
Palmer produced arguably the brightest moment during a poor first 45 when he breezed past Rashford and Casemiro, bursting through the pair as he drove towards United's backline, but his overall display was far from his best.
ATTACK
Noni Madueke - 5/10
Madueke directed a header onto the post inside the opening 15 minutes, but he struggled to make his mark after that and rarely got the better of United left-back Mazraoui.
Nicolas Jackson - 5/10
It was a quiet afternoon for Jackson, who failed to test Onana between the sticks, although he lacked the service from out wide and in central positions.
Pedro Neto - 6/10
Neto looked a bright spark at times when running at United's defense with the ball. He fizzed a decent shot narrowly wide of the far post early in the second half, but he was unable to contribute with much more.
SUBSTITUTES
Marc Cucurella- 6/10
Chelsea looked much more balanced both offensively and defensively when left-back Cucurella came on for Gusto at half time. The Spaniard drifted into central areas at times and looked to offer a threat going forward, but was fairly quiet for the most part.
Enzo Fernandez - 5/10
Came on with 20 minutes remaining and stumbled towards a poor shot that he curled over from the edge of the area.
Mykhaylo Mudryk- 5/10
Came on with 20 minutes remaining and had a couple of nice touches, but he did not offer anything going forward.