Chelsea have Champions League qualification in their own hands and Aston Villa moved into the top five as both teams won in the Premier League on Friday.
The Blues looked as if they were going to drop down to sixth before Marc Cucurella's header earned them a 1-0 win over Manchester United.
Aston Villa, who would have had their fate in their hands had Cucurella not scored, beat Tottenham 2-0.
Unai Emery's side are up to fifth, but sixth-placed Manchester City, one point below them, play Bournemouth on Tuesday (20:00 BST) in their game in hand.