Everton continued their unbeaten start to the season under Ronald Koeman as Shay Given’s unfortunate own goal handed them a 1-0 over Stoke City at Goodison Park.
Phil Bardsley conceded a penalty for tripping Ashley Williams in the box just after half-time and, though Given did brilliantly to tip Leighton Baines' spot-kick onto the post, the ball rebounded into the net off his head.
Stoke pushed for an equaliser in the second half with Marko Arnautovic their primary threat but were unable to beat the excellent Everton goalkeeper Maarten Stekelenburg.
After a scrappy opening, the game's first moment of real quality came from Kevin Mirallas on the edge of the box when he skipped past Glenn Whelan and drilled a low shot which Given got down smartly to save.
It was Stoke who looked more composed in the first quarter with Joe Allen seeing a lot of the ball as he enjoyed a free role in midfield.
Peter Crouch started for the Potters after his hat-trick against Stevenage in the EFL Cup on Tuesday and Stoke targeted him with floated crosses from the right.
He was isolated with 19-year-old Mason Holgate at the back post on one of those balls from Bardsley but elected to attempt a scissors kick and that allowed the Everton defender to head clear.
The best chance of the first half fell to Ashley Williams in the 24th minute when he headed a corner downwards past Given but Crouch hooked the ball clear off the line.
Yannick Bolasie, who was starting his first league game for Everton, cut a frustrated figure on the right wing during the first quarter but a switch to the left helped him grow into the game as the game wore on and Everton finished the half well on top.
Everton picked up where they left off in the second half with Barkley going close with a low shot that flew inches wide before Holgate and Lukaku combined for a lovely one-two in the box that forced Ryan Shawcross to make a brilliant challenge to prevent a certain goal.
It was from the resulting corner that the pivotal moment in the game came as Bardsley clipped Williams' heel as the pair ran towards the ball and Everton went ahead thanks to Given's misfortune.
Stoke were almost level just before the hour mark as Arnautovic got onto the end of a flick on from Crouch and found a yard of space before drilling a low shot which Stekelenburg did brilliantly to save up onto the crossbar.
Everton almost made it two on 78 minutes when Barkley showed brilliant skill to flick the ball past Shawcross to get one-on-one with Given, but the Irishman got down well to save his low shot.
Stoke went straight up the other end and almost scored again. Arnautovic got clean through on goal but, at a tight angle, elected to square the ball to substitute Jonathan Walters, who was unmarked five yards out, but the Irishman was not anticipating the pass and could not adjust in time.
Everton held on to win and will go into the international break with seven points from their opening three fixtures while Stoke sit bottom of the table with just one point on the board so far.
Player ratings
Everton: Stekelenburg (8), Holgate (7), Williams (8), Jagielka (6), Baines (6), Barry (6), Gueye (7), Barkley (7), Bolasie (7), Mirallas (6), Lukaku (6)
Subs used: Kone (5), Funes Mori (6), Davies (N/A)
Southampton: Given (7), Bardsley (5), Shawcross (6), Cameron (5), Pieters (6), Whelan (5), Imbula (5), Allen (6), Diouf (5), Arnautovic (7), Crouch (6)
Subs used: Walters (4), Bojan (5), Ahmed (5)
Man of the Match: Ashley Williams