New signings Jack Grealish and Kiernan Dewsbury-Hall added to the excitement on the pitch, and Iliman Ndiaye created the first scoring opportunity for Everton. However, Ndiaye's shot was unable to beat Brighton's goalkeeper, Bart Verbruggen.
Brighton tried to spoil the party, but their attempts were unsuccessful. Kaoru Mitoma hit the crossbar with a stunning volley, and Danny Welbeck missed an open goal in front of him. Despite the visitors' efforts, Everton's destiny was to score first.
Grealish drifted in from the left and passed the ball across the face of the goal, where Ndiaye came in to prod the ball goalward, making Merseyside history. Tim Iroegbunam could have made it two soon after, and Fabian Hürzeler's men felt unlucky not to be at least level at the break.
Jan Paul van Hecke struck the post, and Matt O'Reilly missed a huge opportunity to beat Jordan Pickford. The hosts forgot about their missed chances during the break and scored their second goal on 52 minutes.
Idrissa Gueye's inventive ball out to the left was taken by Grealish, who laid it back to James Garner, who rocketed the ball inside Verbruggen's near post. Brighton struggled to chase the deficit until the last 15 minutes, when Minteh's shot hit Dewsbury-Hall's hand in the area, but Pickford denied Welbeck from the penalty spot.
The final moments saw the visitors give up hope, and substitutes Beto and Dwight McNeil both went close before the final whistle. Brighton's lack of composure in front of goal was evident, but Everton produced a display worthy of this venue.
The team will hope it's a sign of things to come this season, while Brighton has now failed to win either of their opening two Premier League fixtures for the first time since 2017.