Winning the Europa League also offers Arsenal and Chelsea the safety net of Champions League qualification should they fail to make the top four in the Premier League.
Arsenal star Mesut Ozil took to Twitter to celebrate his sides victory over Manchester United and included a dig at Jesse Lingard.
Manchester United slipped to their first domestic defeat under Ole Gunnar Solskjaer at Arsenal.
Manchester United have made up an 11-point gap to the Premier League top four under Solskjaer, but their Champions League status for next season is still far from assured.
Arsenal must now turn the tie around in the second leg at the Emirates Stadium next Thursday if they are to progress any further in the Europa League.
Harry Kane's contentious penalty 16 minutes from time ensured Tottenham maintain a four-point lead over Arsenal in the fight for top-four finish.
Manchester United and Liverpool played out a goalless draw, while Arsenal returned in top four with a 2-0 win over Southampton in the Premier League.
Both Premier League clubs Arsenal and Chelsea were initially drawn to be at home in the first leg.
Chelsea face Manchester City in the Carabao Cup final on Sunday, then take on Tottenham in the Premier League.
Chelsea face Manchester United in the FA Cup on Monday, before facing City again in the League Cup final on February 24.
Esha Gupta was heavily criticised after she posted screenshots of a racist exchange about Arsenal winger Alex Iwobi between herself and a friend.
Manchester United's 1-0 win helped them move above Arsenal into fifth while Manchester City beat Arsenal to leapfrog Tottenham into 2nd.
Gonzalo Higuain showed why he has a stellar scoring record over the past decade in Spanish and Italian football with two excellent finishes to open his Premier League account.
Manchester United beat Arsenal in the 4th round and they face another tough tie after Monday's draw paired them with Maurizio Sarri's Chelsea.
Manchester United's winning run under Ole Gunnar Solskjaer is now eight games in all competitions.
Unai Emery's side Arsenal host Manchester United in the FA Cup fourth round on Friday.
Liverpool's haul of 60 points from 23 matches tops the Reds' previous best tally of 59.
Saturday's early kick-off saw teenage midfielder Declan Rice score his first West Ham goal in a 1-0 win at home to London rivals Arsenal.