Another error from David de Gea allowed Marcos Alonso to cancel out Juan Mata's opener and claim what could be a valuable point in the quest for Champions League qualification.
United started the day knowing anything less than a win would leave them needing a few favours in the final two matches of the season, and they deservedly went ahead in the first half after producing a far better performance than they have managed in their recent run of seven defeats in nine games in all competitions.
United's fast start yielded a goal after 11 minutes - their first from open play since April 2 - when Mata, on his 31st birthday, turned in Luke Shaw's cutback after a fine pass from Romelu Lukaku.
Chelsea responded with a period of possession, but the recalled Eric Bailly could have made it 2-0 with a header he glanced just past the right-hand post.
The visitors managed to draw level moments before the break, though, as Alonso squeezed in the rebound after De Gea failed to hold Antonio Rudiger's speculative strike from 35 yards out.
3 - David de Gea has made three errors leading to goals in his last four games in all competitions for Manchester United - as many as in his previous 123 matches combined for the Red Devils. Sloppy. #MUNCHE pic.twitter.com/Tbq59cYSU7— OptaJoe (@OptaJoe) April 28, 2019
The second half was disrupted by a succession of injury problems, with Rudiger and Marcus Rashford unable to fight through the pain barrier and Bailly then helped off after an awkward collision with Mateo Kovacic.
Marcos Rojo had a header cleared off the line by Pedro in injury time, while De Gea saved from Gonzalo Higuain, but United will now need to beat Huddersfield Town and Cardiff City in their final two matches and hope for some help elsewhere if they are to secure Champions League football for next season.
What does it mean? Top four in Chelsea's hands
Thanks to Leicester City's 3-0 defeat of Arsenal earlier, the draw gives Chelsea a two-point cushion to Arsenal and keeps them three above United with two games left.
It means Maurizio Sarri's men, along with Tottenham, must now be clear favourites to finish third and fourth, even though the Blues have potentially tricky games against Watford and Leicester to come.
Mata reminds United what they could miss
It seems likely Mata will leave Old Trafford at the end of the season, but this was a timely reminder - against his old club, no less - that he still has plenty of quality to offer.
De Gea dilemma continues
Solskjaer was adamant he would not drop De Gea for this match. After his third costly error in four games, and with the top four still just about within United's reach, he might have no choice.
Key Opta facts
- Chelsea and Man Utd have drawn both Premier League meetings in a single season for the fifth time, most recently doing so in 2015-16.
- Man Utd attempted just seven shots against Chelsea – since 2003-04, they’ve only had fewer in a Premier League game at Old Trafford on four previous occasions.
- Chelsea are winless in their three games against Man Utd across all competitions this season (D2 L1) – the last time they faced them as many times in a single campaign without a single victory was in 2002-03 (D1 L2).
- Man Utd have kept a clean sheet in just 11% of their league games at Old Trafford this season (2/18), their lowest percentage in a single campaign since 1962-63 (9.5% - 2/21).
- Juan Mata is the third Man Utd player to score a Premier League goal on his birthday, after Wayne Rooney (vs Arsenal in 2004) and Anthony Martial (vs Arsenal in 2018).
- Since his Premier League debut for Chelsea in September 2016, Marcus Alonso has scored more goals than any other defender in the competition (15).