Casemiro's spectacular first-half goal proved decisive as Manchester United won 1-0 away to Bournemouth on Saturday to move within sight of Champions League qualification.
Erik ten Hag's side would have been assured of a place among Europe's elite next season had Liverpool lost to Aston Villa but their arch-rivals came from behind to secure a 1-1 draw.
Even so United now need just one point from their remaining two Premier League games this season - with the London duo of Chelsea and Fulham visiting Old Trafford on Thursday and a week on Sunday respectively - to be assured of a Champions League place.