Former Saints man Theo Walcott and Richarlison each struck before half-time, with the visitors the architect of their own undoing.
Mark Hughes, who was without Mohamed Elyounoussi and Jan Vestergaard through injury and illness, respectively, reverted to a back four following the switch against Burnley.
Centre back pairing Wesley Hoedt and Jack Stephens and the rest of the Saints defence, however, struggled to contain a rampant Richarlison from tallying his third goal of the season.
Walcott would turn from goal scorer to provider to set up Richarlison just after the half hour mark to make it 2-0, as the Brazilian headed in his teammate’s delivery.
Ings lifted Southampton in the second-half and came close only to be denied at the near post by Jordan Pickford.
Minutes later, the striker pounced first to slot in James Ward-Prowse’s corner kick from close-range to pull Southampton within a goal.
But Southampton never managed to find a breakthrough to draw level, and nearly fell behind further when Walcott had a goal ruled out for offside.
Everton: Pickford, Baines, Keane, Holgate, Coleman, Schneiderlin (Davies 24), Gueye, Richarlison (Niasse 86), Sigurdsson, Walcott, Tosun (Calvert-Lewin 75).
Unused subs: Stekelenburg, Zouma, Kenny, Lookman.
Goals: Walcott (15), Richarlison (31).
Southampton: McCarthy, Bertrand, Hoedt, Stephens, Cedric, Lemina, Romeu (Gabbiadini 72), Redmond, Ward-Prowse (Armstrong 84), Austin (Long 58), Ings.
Unused subs: Gunn, Yoshida, Targett, Hojbjerg.
Goals: Ings (54).
Bookings: Hoedt (17), Lemina (19), Romeu (36), Cedric (44), Stephens (59).