Goals from Demarai Gray and Dominic Calvert-Lewin earned the Toffees victory.
Everton jumped into the embryonic table’s top four thanks to two wins and a draw, with Gray claiming his second goal of the season and Calvert-Lewin making it three in three games.
Brazil forward Richarlison had a petulant strop when denied the chance to take a penalty, with Calvert-Lewin instead coolly dispatching the spot-kick.
Boss Rafael Benitez insisted on Friday he was “99.9 per cent” sure Richarlison would stay at Goodison Park despite strong interest from Paris St Germain.
The 24-year-old appeared ready to tangle with anyone in his way at the Amex Stadium, but looked sharp and certainly never lacked passion.
Captain Seamus Coleman won the penalty that Richarlison so wanted to take, and the skipper sorted out the mess for Calvert-Lewin stepping up as per team orders.
Benitez won the tactical battle with Brighton counterpart Graham Potter, as the Seagulls surrendered their 100 per cent start to the season.
Brighton’s 3-1-5-1 in possession ultimately left too much stress on the Seagulls when they lost the ball, which in the first half proved far too frequent.
The excellent Yves Bissouma was left with too many gaps to plug at the base of midfield when Brighton lost the ball, because his deep-lying partner Adam Lallana was typically stranded too high upfield.
Couple that shortcoming with Brighton’s lack of genuine rearguard pace, and Benitez knew exactly how to open up the hosts.
The warning signs were there throughout the opening period, despite Brighton creating in fits and starts, albeit without ever cutting loose.
When the Everton breakthrough came however, it proved alarmingly simple. Gray picked up possession just inside the Brighton half and set off goalwards.
Every time he would have expected to be challenged, no intervention came.
The former Leicester man just put his head down and powered on, and when he breached the box, he simply swept the ball past the helpless Robert Sanchez.
Potter brought on Joel Veltman at the start of the second half, switching to a back four in a bid to spark Brighton into life.
The change so nearly yielded immediate dividend, with Veltman rolling in a dangerous low cross that the slipping Leandro Trossard could only scuff when he should have scored.
Pascal Gross then forced goalkeeper Jordan Pickford into parrying a low-struck free-kick, before Veltman blasted high over the crossbar from 20 yards.
Veltman’s strong start was entirely undone when he felled the onrushing Coleman to gift Everton a fully-deserved penalty.
Richarlison shaped to take the spot-kick but was overruled, leaving the Brazil forward enraged and tangling with team-mates.
The unruffled Calvert-Lewin ignored the sideshow and slotted home to put Everton 2-0 to the good and in total control.
Only Lewis Dunk’s last-ditch sliding challenge denied Gray a clear run at a third goal, before Sanchez saved well from Abdoulaye Doucoure.