It is going to be a long season for Iain Dowie and Crystal Palace as Everton recovered from their humiliating defeat against Arsenal last weekend.
Mark Hudson's header gave Palace the perfect start after nine minutes, but Everton pounced on defensive errors by the home side as Thomas Gravesen scored twice and Marcus Bent added a late third.
A lively first half saw the Eagles make a great start on the return of their Premiership after a six-year gap. Andy Johnston led the way as he conjured up the chance that led to the opening goal.
Joonas Kolkka on the left fed Johnson on the edge of the box and his shot was blocked. However the ball then kindly took Wayne Routledge just inside the area and the Palace wideman easily slipped past Gary Naysmith before crossing for Hudson to head the home side in front.
A few minutes later Johnson was in the action again, racing on to Dougie Freedman's pass then beating visiting keeper Nigel Martyn only to see his shot blocked by Toffees skipper Alan Stubbs.
The Toffees were having real problems coping with Johnson and Freedman at this stage of the game, but Everton were back in it after a crazy mistake by Palace's keeper Julian Speroni.
The Argentinian presented Everton with their equaliser with the daftest piece of goalkeeping you are likely to see in the Premiership this season.
He had already put Tony Popovic under pressure with a risky throwout, but the Palace centre-half still managed to return the ball to Speroni. A simple clearance upfield was instead preferred to some fancy footwork.
However, Speroni, a summer signing from Dundee, dithered before losing the ball to Kevin Campbell and then tripped the Everton hitman.
From the spot Gravesen made no mistake with a right-foot shot past Speroni which nestled in the right-hand corner of the net.
After the break Palace lost their way while Everton's Gravesen and Lee Carsley took a much tighter grip of the midfield.
Indeed Everton were having their best spell as Palace, so confident in the first half, were struggling with passes all to often going astray and movement from their players almost non-existent.
Everton took advantage and on 62 minutes Gravesen picked up a sloppy clearance and from 20 yards picked his spot with a curling shot past Speroni and into the top far corner.
Bent, a Palace favourite last year, struck a tremendous volley which brought a brilliant reflex save from Speroni.
The Toffees were looking comfortable, but Naysmith was shown the red card on 70 minutes for his second bookable offence, as he pulled down Routledge after the Palace youngster tried to pass him with a cheeky lob over his head.
Still Bent made sure there was to be no last-minute panic with a neat finish after Gravesen drilled a great pass into his path.
Speroni left his goal to narrow the angle, but Bent coolly struck the ball wide of the keeper's left hand to ensure the travelling fans were sent back up the M1 in good spirits.
Man of the Match: Thomas Gravesen - The Danish hardman controlled the midfield along with Lee Carsley and his two goals ensured that the Toffees took all three points at Selhurst Park.