James McFadden's rich vein of form continued at Hillsborough as his second-half double sent Sheffield Wednesday spinning out of the Carling Cup.
The Scotland international swept home at the far post in the 58th minute to warm the Everton fans after a dismal first half and then popped up in an identical position to head home Phil Neville's superb cross to seal the third-round tie with seven minutes remaining.
McFadden, whose stunning effort for his country recently accounted for France in a European Championship qualifier, then set up a third goal, for Ayegbeni Yakubu 60 seconds later.
Sheffield Wednesday boss Brian Laws made five changes to his starting line-up.
Defenders Peter Gilbert and Richard Hinds, wingers Jermaine Johnson and Wade Small and striker Marcus Tudgay all returned as the Owls sought to build on their first win of the season against Hull last weekend.
Everton counterpart David Moyes also rang the changes. James McFadden, skipper Alan Stubbs, Nuno Valente, Ayegbeni Yakubu and Lee Carsley were all recalled for the third round clash.
New loan signing Graham Kavanagh made his second start under the floodlights at Hillsborough, which was by no means full and a reflection of the Owls' near-disastrous start to the new season.
Winger Jermaine Johnson dragged an angled shot from the edge of the area wide, while Yakubu blazed high and way off target from 25 yards at the other end.
Neither side mustered a clear-cut chance in the first 20 minutes and Johnson mis-directed another low drive after being teed up by former Everton starlet Francis Jeffers.
Free of injury at last following his summer switch to Hillsborough, the former Arsenal and Blackburn striker then set up Marcus Tudgay with quick feet on the edge of the area, but the latter's effort was deflected for a corner.
Two minutes after the break it was evident substitute Neville - on for Hibbert - was eager to up the tempo.
Jeffers' backheel almost set up Small and then Phil Jagielka unleashed a trademark 30-yard shot that Lee Grant easily held.
Livewire Jeffers forced a corner from Everton goalkeeper Stefan Wessels when latching on to a long ball, but the visitors hit Wednesday on the break to take a 58th-minute lead.
Steven Pienaar threaded a fine pass into Yakubu's path down the right and his curling low cross to the far post was met by McFadden, who comfortably side-footed home his second goal of the season for Everton.
The Scot, whose two goals for Scotland in the Euro 2008 qualifiers catapulted him to hero status north of the border, then tried an audacious chip from 20 yards that landed on top of Grant's net.
Leighton Baines replaced Valente in the 64th minute and Owls boss Laws responded by sending on Deon Burton for Johnson three minutes later.
Laws then sent on another striker, Akpo Sodje, in the 72nd minute, with Jeffers sacrificed after making little impact against his former club.
Kavanagh curled a 30-yard free-kick just over the crossbar and then Burton was guilty of missing the home side's best chance of the evening.
Sodje bustled his way onto the ball and set Small charging down the right and, when he stepped over the winger's cross, Burton blasted his shot from eight yards over with just Wessels to beat.
Glenn Whelan was inches away with a raking drive that left Wessels helpless as Wednesday briefly threatened to haul themselves back into the game.
But Neville raced away down the right and his superb pinpoint cross to the far post was headed home by McFadden.
And within 60 seconds the Merseysiders made it 3-0. This time McFadden turned provider, picking the ball up deep in
Wednesday's half and playing a defence-splitting pass inside the full-back to Yakubu, who calmly steered the ball beyond Grant into the keeper's bottom left-hand corner.
