Romelu Lukaku's brace set Everton on course for an impressive first win of the season as Roberto Martinez's side secured a surprisingly comprehensive victory at Southampton.
Both sides' Premier League campaigns began with 2-2 draws, although Saints' result at Newcastle brought a far more positive reaction than the Toffees' underwhelming comeback draw at home to promoted Watford.
Some disgruntled fans called for chairman Bill Kenwright and the board to leave Everton in a banner flown over St Mary's, but those frustrations were forgotten for 90 minutes at least as Lukaku's double and a classy Ross Barkley effort secured an impressive 3-0 win.
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It was some way to end a six-match winless run on the south coast and dampened the feel-good factor around St Mary's, where late owner Markus Liebherr was remembered five years after his passing.
Everton dashed Saints' hopes of marking the occasion with a win as Lukaku nodded home a superb opener midway through the first half - a goal one home fan may well have applauded given the Belgium international made his way into the stands during the warm-up to check on her after his wayward shot hit her.
The £28 million striker continued to boss the hosts' back-line and added another as half-time approached.
Barkley was the architect with a fine pass and added extra gloss to the scoreline as the match came to a close, curling home a fine third in front of England manager Roy Hodgson.
The game will have made uncomfortable viewing for Southampton manager Ronald Koeman, back on the sidelines after missing the trip to Newcastle following Achilles surgery.
The hosts started well enough, with Graziano Pelle, Sadio Mane and Dusan Tadic having efforts of varying quality before Matt Targett forced Tim Howard into his first save of the match in the 17th minute.
The England Under-21s left-back, deputising for the injured Ryan Bertrand, was already in Michael Oliver's notebook by that point having hacked down Lukaku in full flight.
Barkley's free-kick was deflected behind for a corner and Arouna Kone's shot from the resulting corner was blocked, but Martinez's side managed to break the deadlock in the 22nd minute.
Saints won a corner after Howard smartly denied Mane but Everton broke at speed from it, with Kone played down the right and crossing for Lukaku to head in off the underside of the bar.
It was a sucker punch Saints failed to respond to, with James McCarthy seeing a cross-shot kept out before Tom Cleverley wasted a gilt-edged chance to score after Barkley's initial effort was saved.
Everton were not made to pay for that missed opportunity, though, as Barkley played through Lukaku, who confidently slotted past Maarten Stekelenburg as half-time approached.
Saints were all too easily being carved open and Koeman acted at the break, bringing on defensive midfielder Oriol Romeu just days after his arrival from Chelsea.
The Spaniard soon had a booking but the hosts were now looking more confident, with Jose Fonte heading wide and Pelle denied by a last-ditch challenge and then a save soon after.
That high-tempo start soon petered out but Saints were still having chances, with Howard denying Mane from long range.
They could not reduce the deficit, though, and Everton pulled further ahead six minutes from time, with Barkley curling home at the end of a fine team move after impressively cutting inside.