Romelu Lukaku scored twice as Everton made light of a poor record at Southampton to run out 3-0 winners at St Mary's Stadium.
With just one victory from their previous 14 Premier League visits, history weighed heavily against Everton and goalscoring hero Lukaku endured an inauspicious warm-up when his wayward shot struck a fan, prompting the striker to head into the stands to apologise.
He proved more accurate once the action got under way, netting a first-half double as Roberto Martinez's men demonstrated their threat on the counter-attack.
The match turned on a fine Tim Howard save, which came less than 60 seconds before Lukaku's headed 22nd-minute opener, while the Belgium forward's second goal also arrived at the end of a quick break.
Ross Barkley added a third late on with a crisp finish to bring further pain to Southampton manager Ronald Koeman, who returned to the dugout on crutches after missing the 2-2 draw at Newcastle United last weekend.
Lukaku signalled his intent early on, his powerful run halted by Matt Targett's foul just outside the area before Barkley's free-kick clipped the wall and deflected over the crossbar.
Everton were pressed into defensive action in the 14th minute when Graziano Pelle's downward header picked out Dusan Tadic, but his shot was blocked and the visitors scrambled the ball clear.
Pelle, with three goals in the opening three games of the season, then failed to connect properly with a back-post header and flicked it harmlessly wide of Howard's right-hand upright.
The hosts continued to force the issue and Sadio Mane brought an excellent stop from Howard with a low close-range effort, before Southampton were caught on the break.
Barkley set Arouna Kone – the visitors' only change from the opening day after his late leveller from the bench against Watford – free down the right following a Southampton corner and his superb delivery was expertly headed home by Lukaku, who was quick to acknowledge the quality of the assist.
Martinez's men should have extended their lead just before the half-hour mark, but Barkley's tame strike from the middle of the area was saved by Maarten Stekelenburg and Tom Cleverley put the rebound wide.
Lukaku did make it 2-0 on the brink of half-time, though, stroking his shot past Stekelenburg after gathering Barkley's pass.
New signing Oriol Romeu was introduced for Tadic for the second half and Koeman's charges started brightly, with Pelle's half-volley stinging Howard's palms.
The Italian carried his side's most potent threat, heading another chance over the bar in the 66th minute as Southampton looked to breach an Everton outfit with only one clean sheet in their last 17 away league matches.
Mane went close, bringing a full-stretch save from Howard from distance, but Barkley's fine right-footed finish put the result beyond doubt in the 84th minute.
For Martinez, who has promised new arrivals, it was a demonstration of the quality already at his disposal, while Southampton's focus will now switch to the first leg of their UEFA Europa League qualifier against FC Midtjylland on Thursday.