Everton saw off an intense second-half fightback from Leeds to seal a vital three points in their race for European football next season.
Gylfi Sigurdsson opened the scoring for the visitors when he turned home Lucas Digne's cross after the Leeds defenders failed to react in time to clear.
Dominic Calvert-Lewin scored his 12th Premier League goal of the season to double Everton's lead when he headed past Illan Meslier.
Raphinha halved the deficit just three minutes after the restart when he fired past Everton goalkeeper Robin Olsen after being set up by Patrick Bamford.