Mikel Arteta's men have now picked up just one point in their past three games as their title push quickly runs out of steam.
Manchester City's second successive draw in the league was especially frustrating as Arsenal moved level on points with them with a last-gasp 4-2 win against Leicester a few hours later.
Enzo Maresca made 11 changes from the team that beat West Ham 3-0 on Saturday but could still start around 400 million pounds ($533 million) worth of talent.
Chelsea suffered fresh frustration after blowing the lead in a 1-1 draw against Crystal Palace, while Newcastle beat Tottenham 2-1 on Sunday.
Ex-Liverpool manager Jurgen Klopp had only won two of his 11 away games against Manchester United.
Newcastle defender Kieran Trippier announced his retirement from international football on Thursday after winning 54 caps for England.
Noni Madueke hit a hat-trick as Chelsea crushed Wolves 6-2 to give Enzo Maresca his first Premier League win as Blues boss.
The Argentine was axed this week after just a year in charge despite steering Chelsea to a sixth-place finish and Europe next season.
Tottenham missed the chance to move into the Premier League's top four after a 1-1 draw at West Ham, while Newcastle were also held 1-1 by Everton on Tuesday.
Eddie Howe's men are languishing in 10th place in the Premier League with 10 games to go and any hope of the club's first major trophy since 1969 is over for another year.
Bernardo Silva scored twice as Manchester City beat Newcastle 2-0 to reach the FA Cup semi-finals on Saturday, while Coventry struck twice in stoppage time to stun Wolves 3-2.
Manchester United are aiming to derail Liverpool's bid for a quadruple and salvage a difficult second season for Erik ten Hag in Sunday's FA Cup quarter-final.
Mauricio Pochettino called for the Chelsea fans to trust his players after a 3-2 win over Newcastle on Monday propelled the Blues back into contention for European football next season
Arsenal's free-scoring Premier League form continued as Newcastle were blown away 4-1 at the Emirates on Saturday to move back within two points of leaders Liverpool.
Manchester City can move within one point of Jurgen Klopp's team if they win their game in hand at Bournemouth, while Arsenal must beat Newcastle to stay in touch with the title pacesetters.
Newcastle are up to seventh place as they try to salvage European qualification from a difficult season.
Pep Guardiola said Manchester City showed the heart of champions to fight back to beat Newcastle 3-2 on Saturday thanks to a Kevin De Bruyne masterclass on his return to Premier League action.
Manchester City trail Premier League leaders Liverpool by five points, with a game in hand.