Home boss Carlo Ancelotti reverted to a back four following the FA Cup defeat Liverpool, while the Brazilian and Dominic Calvert-Lewin continued in attack.
Stalwarts Shane Duffy and Lewis Dunk were amongst the five reintroductions for the visitors and Dunk was in the thick of the early action when he pulled down Theo Walcott in the box.
Walcott got an effort away but was undoubtedly impeded. After referee David Coote waved away the protests, a decision that puzzled most at Goodison Park, the VAR agreed with him.
Everton did not lose heart, though, with Richarlison and Bernard looking exceptionally sharp and it was the former who got the only goal of the first half.
Moments after stinging Mat Ryan’s palms, Richarlison broke the deadlock, receiving the ball in the box following an excellent counter-attack before Cruyff-turning away from the defence and curling home off the post.
Brighton were sent out early from the break by Graham Potter and almost had an immediate response when Leandro Trossard struck over, albeit with Coote’s whistle having blown.
Replays suggested it wasn’t a foul by Bernardo in the build-up but Trossard seemed inspired now, smashing off the bar soon afterwards.
That was as close as Brighton came, while Everton thought they had a second when Dominic Calvert-Lewin bundled home, with help from Adam Webster, only for VAR to adjudge the home striker had used his arm to direct the ball goalwards.
The Toffees started to sit back after that and almost paid when substitute Glenn Murray missed the target with two late efforts.
Everton stood strong to claim a deserved three points to make it four unbeaten at home but, on this showing, Brighton may need to watch themselves, with Aston Villa, Bournemouth, West Ham and Watford their next four fixtures.