The win at Goodison Park lifted the Toffees to 36 points and safety, leaving Nottingham Forest, Luton and Burnley in danger with two of them destined to be relegated with Sheffield United.
It was the third straight home victory for Everton, who had eight points deducted this season for two breaches of Premier League financial rules.
IDRISSA GUEYE (Everton)
Gueye scored the only goal as Everton beat Brentford to guarantee their Premier League survival. Gueye, 34, fired home through a crowd of players in the 60th minute for his sixth goal in 189 English top-flight games.
JEFFREY SCHLUPP (Crystal Palace)
Ghana midfielder Schlupp, 31, scored a stunning goal from distance as Palace rescued a point at Fulham. The substitute received a pass from Adam Wharton before hitting a thunderous strike into the top corner in the 87th minute to make it 1-1.
EVAN NDICKA (Roma)
Ivory Coast defender Ndicka returned to action, starting in a Serie A fixture at Napoli after being cleared to play following an on-pitch collapse this month. Ndicka fell to the turf at Udinese with what was initially feared to be heart problems, causing play to be suspended with 18 minutes left and the teams drawing 1-1. However, Ndicka was cleared of any cardiac issues and Roma eventually won the restarted fixture on Thursday thanks to a late goal. On Sunday, he provided the corner from which Tammy Abraham headed in the equaliser in a 2-2 draw in Naples.
ADEMOLA LOOKMAN (Atalanta)
The England-born Nigeria striker scored the second goal of Atalanta's 2-0 win over Empoli. Lookman found the net after a run down the left in the 52nd minute and almost had a second moments later.
AMINE ADLI (Bayer Leverkusen)
Robert Andrich may have equalised with the last kick of the
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