Both sides made fast starts last weekend, each striking within the opening 13 minutes during their respective wins, but there was no such breakthrough here as Tariq Lamptey’s unthreatening cross-shot was the only half-chance in a cagey opening quarter.
Neither side showed much attacking intent in the first period before a rare Everton launch into Brighton’s penalty area resulted in a penalty, with Joël Veltman using his hand to clear the ball.
Fresh from scoring against Tottenham on Sunday, Iliman Ndiaye assumed responsibility from the spot, firing past Bart Verbruggen to give the Toffees their first HT away lead in the PL since October.
A Ndiaye goal was generally a good omen for Everton, who are unbeaten in six games when he has scored this season, but the Toffees faced a determined Brighton response after the break as Kaoru Mitoma’s whipped shot that had Jordan Pickford scrambling before the attempt inched past the post.
Chances for the hosts kept piling up as João Pedro’s deflected effort forced Pickford into a fingertip save and Georginio Rutter’s powerful half-volley flew just wide of the top corner.
That opportunity was Brighton’s last as Everton almost snatched a late second on the counter through Beto, who raced past Jan Paul van Hecke and shot into the side-netting.
After sealing back-to-back away wins, Fabian Hürzeler’s Seagulls will be frustrated at failing to win at home for a fifth consecutive match and the south coast side are now six points off the PL’s European places.
Moyes came into this contest with just one career win over Brighton in 10 attempts, but a typically solid performance from his Everton side put that record to bed as the Toffees sealed successive PL wins for the first time since April 2024.