Johann Gudmundsson put Burnley ahead just five minutes into the contest at Selhurst Park, and Joy Rodriguez doubled the Clarets’ lead five minutes later.
Palace were toothless in attack, and Matthew Lowton scored two minutes after the restart to wrap up the result with plenty of time to spare.
While Palace do not look to be in danger of relegation given they hold a 14-point cushion above the drop zone, the manner of the defeat will alarm Roy Hodgson as the Eagles once again lost without talisman Wilfried Zaha.
A sour note for Burnley was the departure of captain Ben Mee on a stretcher in the 84th minute. He was knocked to the floor after an innocuous coming together with Ayew and had to be replaced after a lengthy delay at Selhurst Park.
Burnley tweeted a more encouraging update on Mee’s condition during stoppage time: “Great to see the skipper now walking and heading to the dressing room, with all medical equipment detached.”