Adam Armstrong, who signed for Southampton on Tuesday, scored on his debut before Everton recovered to spoil the party with three second-half goals.
Richarlison drew the hosts level immediately after the restart before Adboulaye Doucoure and Dominic Calvert-Lewin struck within five minutes of each other.
Saints started a make-shift backline with last season’s regulars Jan Bednarek and Kyle Walker-Peters resigned to the bench in favour of Jack Stephens and newcomer Valentino Livramento.
Romain Perraud was also handed his Saints debut, playing 83 minutes before being subbed for Nathan Redmond with the visitors chasing the game late.
Armstrong combined with his strike partner Che Adams, firing a right-footed shot into the top corner on 22 minutes.
Southampton’s first-half display, which could’ve seen their lead doubled, meant Everton was met with a chorus of boos as the teams departed for half-time.
Richarlison would equalise from close range two minutes after the restart after Andros Townsend’s flick-on teed up the Brazilian.
Doucoure gave Everton a 2-1 lead in the 76th minute with a sensational finish as he turned his defender inside-out before hooking a right-footed shot past a diving Alex McCarthy and into the top corner.
Richarlison then set up Calvert-Lewin for a diving header nine minutes from full-time to seal all three points for Everton’s new manager, Rafa Benitez.
Southampton, meanwhile, have grown all too accustomed to dropping points from winning positions with Ralph Hasenhuttl still searching for the right formula.
Everton (4-2-3-1): Pickford; Digne, Keane, Holgate, Coleman; Richarlison (Gordon), Gray (Yerry Mina), Townsend (Iwobi); Calvert-Lewin
Unused subs: Begovic (GK), Delph, Kenny, Broadhead, Davies, Branthwaite
Goals: Richarlison (47), Doucoure (76), Calvert-Lewin (81)
Bookings: Richarlison (30), Doucoure (77)
Southampton (4-4-2): McCarthy; Perraud (Redmond), Salisu, Stephens, Livramento; Djenepo, Romeu (Diallo), Ward-Prowse, Walcott (Tella); A. Armstrong, Adams
Unused subs: Forster (GK), S. Armstrong, Elyounoussi, Bednarek, Walker-Peters, Valery
Goals: A. Armstrong (22)