James Ward-Prowse fired Saints ahead before Che Adams doubled a deserved lead inside 35 minutes for the hosts, who climbed into fifth place in the table on 10 points through six games.
Stuart Armstrong nearly added a third for a rampant Southampton when he hit the back of the net after linking up with Adams, but the forward was ruled offside in the build-up.
Everton fell from the ranks of the unbeaten after starting the 2020/21 campaign with four wins and a draw from their first five games, but still maintained their position at the head of the table, level with rivals Liverpool.
The visitors had two early chances to break the deadlock, including when Gylfi Sigurdsson rattled the crossbar from distance on 19 minutes, which seemingly shocked Southampton awake.
Nathan Redmond hit an attempt wide of the post at the other end before Oriol Romeu looked to add another stunning goal to his tally only to be denied by Jordon Pickford.
Ward-Prowse gave Southampton the lead nearing the half-hour mark when he played a smart one-two with Danny Ings, who nut-megged his defender allowing his teammate to race onto the ball and smash his shot into the bottom corner.
Adams then made it 2-0 when he turned in Ings’ cross from the right side of the box with a vicious strike that squeaked through Pickford.
With Everton chasing the game, Lucas Digne compounded the situation by being shown a straight red card for a foul on Kyle Walker-Peters 17 minutes from full-time.
The full-time whistle secured back-to-back home wins for Southampton for the first-time in 2020 and a third clean sheet this season.
Southampton (4-4-2): McCarthy; Bertrand, Vestergaard, Bednarek, Walker-Peters; Redmond, Romeu, Ward-Prowse, Armstrong (Diallo 86); Ings, Adams (N’Lundulu 89)
Unused subs: Forster (GK), Stephens, Vokins, Tella, Long
Goals: Ward-Prowse (27), Adams (35)
Bookings: Walker-Peters (57)
Everton (4-4-3): Pickford; Digne, Keane, Mina, Godfrey; Sigurdsson (Gordon 58), Allan, Doucoure (Delph 58); Iwobi (Bernard 46), Rodriguez, Calvert-Lewin
Unused subs: Olsen (GK), Andre Gomes, Davies, Nkounkou
Bookings: Bernard (64), Digne (RED 73), Calvert-Lewin (90+2)