The game turned on an 18th-minute red card to Jarrad Branthwaite for pulling back Ivan Toney, when Everton was leading 1-0 thanks to Dominic Calvert-Lewin’s goal.
Still, Everton — needing a win to guarantee survival — bounced back from conceding an equalizer in the 37th minute because of an own-goal by Seamus Coleman by going ahead again when Richarlison converted a penalty in first-half stoppage time.
Brentford twice in two minutes from the 62nd, through Yoane Wissa and Rico Henry, and substitute Salomon Rondon became the second Everton player to be red-carded after he launched himself studs-first at Henry in the 88th.
Everton stayed two points above the bottom three and has two games remaining, against Crystal Palace at home on Thursday and Arsenal away next Sunday.
Leeds is a point behind Everton and has one game left, at Brentford on the final day, while third-to-last Burnley still has Aston Villa and Newcastle to play. -AP