Goals from Theo Walcott and the Toffees' record signing ensured that Marco Silva opened his home account on Merseyside with three points despite Danny Ings doing his best to inspire a second-half revival for the Saints.
The Blues treated the Everton faithful to some commendable energy in the opening exchanges and the hosts might have taken the lead after just five minutes when Gylfi Sigurdsson found Michael Keane inside the box, although the defender could only head into the arms of Alex McCarthy.
Southampton appeared disjointed in the final third and their best early chance was to be conjured by a testing set piece from James Ward-Prowse, whose delivery saw Charlie Austin glance a header wide of the target with Jordan Pickford struggling to make ground.
Mark Hughes's charges fell asleep at a free kick in the 15th minute and Everton soon made them pay. Leighton Baines faked to shoot before feeding a short pass into Morgan Schneiderlin, who then flicked a clever ball into space for the run of Walcott, allowing the winger to lift a deft finish over McCarthy and make it 1-0 to the Blues.
Saints' early energy began to drift as Everton took control of proceedings, but the visitors were handed a crucial chance when Pickford spilled a Cedric Soares shot straight into the path of an unmarked Ings.
The striker should have lashed his effort into an almost-empty net, but England international Pickford had other ideas as he produced a stunning reflex save to send the forward's shot up onto the crossbar and away from danger.
Everton capitalised not long after when Walcott broke down the right to cross into the middle, where Cenk Tosun's movement freed up space for Richarlison, who bagged for the second game in a row when he beat Soares in the air to head Everton firmly into the driving seat in the 31st minute.
Saints were much improved after the break and they finally found a route back into the game through Ings, who pounced on Mario Lemina's knockdown from a corner to turn the ball home and hand his side a lifeline.
Everton were shaken as the visitors gained ground on Merseyside, but the Toffees might just have put the game to bed when Walcott broke free of Jack Stephens only to see his adroit finish ruled out for a close offside call.
The former Arsenal winger should have sealed the three points moments later too, although the 29-year-old somehow skewed his effort wide of the post with the goal gaping, after latching onto an eye-catching one-two with Sigurdsson.
With the game moving into the dying embers Southampton continued to force the issue in search of an equaliser, but Everton eventually held firm to close out a hard-earned three points that leaves the Toffees unbeaten in their first two league games for a sixth season running.
EVERTON (4-2-3-1): Pickford; Coleman, Keane, Holgate, Baines; Gueye, Schneiderlin (Davies 24'); Walcott, Sigurdsson, Richarlison (Niasse 86'); Tosun (Calvert-Lewin 75')
SOUTHAMPTON (4-4-2): McCarthy; Soares, Stephens, Hoedt, Bertrand; Ward-Prowse (Armstrong 84'), Romeu (Gabbiadini 72'), Lemina, Redmond; Austin (Long 58'), Ings