The full-back found the back of the net with three minutes of normal time left to play to maintain the Toffees' fine run of form
Sam Allardyce's search for a first Premier League victory as Crystal Palace manager goes on after Seamus Coleman's late effort secured a dramatic 1-0 victory for Everton at Selhurst Park.
Ronald Koeman's side had the better of Saturday's encounter but, despite a glut of excellent chances, could not replicate the clinical finishing from their 4-0 thumping of Manchester City last time out, with Wayne Hennessey in top form in the Palace goal.
Though he produced a string of quality saves to keep the visitors at bay - a finger-tip stop from Ramiro Funes Mori the highlight - Hennessey could do nothing to prevent Coleman thumping in an 87th-minute winner.
Palace, who slipped into the relegation zone prior to kick-off thanks to Swansea City's shock victory at Liverpool, had started in lively fashion - Christian Benteke hitting the woodwork - and the hosts would have taken a late lead themselves if not for Joel Robles excellent save.
It appeared that Everton would have to settle for a share of the spoils, but Coleman came up with the goods late on, ensuring a fourth win in six league fixtures for Ronald Koeman's men.
The defeat keeps Palace two points adrift of safety, while Everton move within five points of sixth-placed Manchester United, who drew at Stoke City.
Benteke's double ensured FA Cup progression for Palace against Bolton Wanderers, and the Belgian went agonisingly close to putting the hosts ahead early on this time around.
Former Liverpool forward Benteke, who netted in the reverse fixture at Goodison Park in September, expertly headed James McArthur's excellent cross goalwards, leaving Robles flat-footed, only for the ball to bounce away off the crossbar.
Everton responded well, Hennessey pulling off fine saves to deny Kevin Mirallas and Ross Barkley as the visitors began to assert some authority.
Barkley looked to have put Koeman's side ahead having hammered home on the rebound after Romelu Lukaku - making his 150th Everton appearance - had hit the post, but the England midfielder was rightly flagged offside.
Palace survived another scare soon afterwards, Hennessey reacting superbly to turn Funes Mori's rasping effort over.
Hennessey was beaten shortly after the restart, though, as Barkley's low strike flashed across the face of goal, whistling just wide of the upright.
Barkley went close again moments later, sliding a cross-cum-shot wide before Lukaku headed over from Everton's next attack.
Looking to capitalise on Everton's strong start to the second half, Koeman introduced Morgan Schneiderlin on the hour-mark, while youngster Ademola Lookman also came on.
Scott Dann thought he had claimed a vital win for Palace with 11 minutes remaining, but Robles was on hand to parry the defender's header wide with an instinctive stop.
And Palace were duly made to pay when, at the culmination of a fantastic run, Coleman powered a venomous finish high into the roof of the net.