Everton have secured a huge victory in their bid to survive and have also damaged their hopes for the top four in Manchester United with a 1-0 victory in the Premier League on Saturday.
Anthony Gordon's shot from the edge of the penalty spot diverted the net from the stretched leg of United full-back Harry Maguire in the 27th minute at Goodison Park.
It was another unfortunate game for United, which saved two fine saves from Jordan Pickford - both in the efforts of Marcus Rashford - at the start of the game and frustrated the strong defense and sometimes defended Everton in the second half.
Anyone who is a full-time replacement for interim manager Ralf Rangnick - Ajax's Erik ten Hag looks to be a favorite in the job - will come to Old Trafford with United out of the Champions League and may not be in any European competition.
United sit three points behind fourth- and fifth-placed teams - Tottenham and Arsenal respectively - and the two London clubs have games in hand.
Things look very good, however, for Everton, who have returned from a disappointing loss to Burnley on Wednesday to remove four points from the bottom three as the team looks to avoid getting out of the top flight for the first time since. 1954.
Everton's home form raises hopes they can stay. Frank Lampard's team has won five of their last seven games at Goodison Park in all competitions.