The script stayed true for Southampton who suffered a third-straight league defeat for the first time since 2014 following a 3-0 drubbing at Everton.
Jay Rodriguez and Nathan Redmond failed to take advantage of clear-cut chances before being punished by three second half goals from Everton.
Ronald Koeman had promised his former employer they’d see a different side, but the hosts were void of worthy opportunities until substitute Enner Valencia’s goal on 73 minutes opened the flood gates.
Southampton -- playing their third match in six days -- made six changes and were without the suspended and in-demand Virgil van Dijk.
Despite the opening 12 minutes being disrupted by injuries, which enforced changes by both managers, Ross Barkley saw his early effort palmed away by Fraser Forster.
Southampton, who mounted pressure with successive corners, was nearly caught on the break when Romelu Lukaku raced in on goal only to be pushed wide by Jack Stephens on 18 minutes.
Rodriguez’s attempt in the 39th minute was indicative of an opening half that lacked quality when he created space along the edge of the box before sailing a shot over the bar.
Southampton’s best opportunity of the second half came on 69 minutes when Rodriguez played Redmond alone on goal, but Joel Robles did well to make the save.
Valencia, whose introduction changed the tide, then pounced on the rebound at the other end four minutes later to make it 1-0 after Forster had denied Lukaku’s close-range header.
Lukaku couldn’t double the lead when he curled over the bar from the edge of the box, but Leighton Baines scored from the penalty spot 10 minutes from full-time.
Rodriguez nearly brought one back for the visitors, but Lukaku made it a comprehensive victory with a thumping effort to the top corner.
Everton: Joel, Baines (c), Funes Mori, Williams, Coleman, Gana, Davies, Lennon (Valencia 61), Barkley (Barry 84), Calvert-Lewin (Mirallas 12), Lukaku.
Unused subs: Hewelt (GK), Jagielka, Cleverly, Holgate.
Goals: Valencia (73), Baines (80 PEN), Lukaku (89).
Southampton: Forster, McQueen, Yoshida, Fonte (c), Cedric (Stephens 6), Romeu, Clasie (Long 77), Ward-Prowse, Redmond, Tadic (Boufal 66), Rodriguez.
Unused subs: Lewis (GK), Bertrand, Reed, Davis.
Bookings: Ward-Prowse (40).