Joleon Lescott headed them in front after six minutes and Steven Pienaar slotted in the second shortly after the break to leave Middlesbrough rueing several missed chances.
Everton, who had lost their previous two league games, have 13 points from eight matches, six behind leaders Arsenal. Boro have eight points.
Struggling Tottenham Hotspur face Aston Villa in Monday's Premier League match.