Richarlison scored in the ninth minute after linking up with Gylfi Sigurdsson, whose through ball split the defence and allowed the winger to round the goalkeeper before slotting into an empty net.
Fraser Forster replaced Alex McCarthy between the sticks while Southampton was without Oriol Romeu, who will miss the remainder of the season with a broken ankle sustained in the loss at Leeds.
Moussa Djenepo and Jannik Vestergaard each had a chance to draw Saints level late on, but the winger fired wide of the post while the defender was denied by Jordan Pickford.
Southampton has lost back-to-back league games after picking up a point over Chelsea, which had ended a historic run of six-straight defeats.
Saints once sat at the top of Premier League, but now sit just seven points above the relegation zone on 30 points from 26 games.
Everton (4-3-1-2): Pickford; Digne, Godgrey, Keane, Holgate; Gomes (Iwobi 87), Allan, Doucoure; Sigurdsson; Richarlison (King 90+1), Calvert-Lewin
Unused subs: Virginia (GK), Bernard, John, Broadhead, Astley, Nkounkou, Onyango
Goals: Richarlison (9)
Southampton (4-4-2): Forster; Bertrand, Salisu (Tella 63), Vestergaard, Bednarek; Redmond (Watts 88), Armstrong, Ward-Prowse, Djenepo; Ings, Adams (N’Lundulu 77)
Unused subs: McCarthy (GK), Stephens, Ferry, Ramsay, Jankewitz, Chauke
Bookings: Armstrong (77), Tella (80)