The Toffees were in the relegation zone when Marco Silva was sacked in December, but victory against Palace, which has now lost three in a row, leaves Everton just five points behind fourth-placed Chelsea.

Bernard put Everton ahead in the 18th minute when he volleyed home Theo Walcott's delivery and the hosts remained in charge until early in the second half, as Jordan Pickford allowed Christian Benteke's effort to go under him.

Everton was back in front soon after, however, Richarlison darting through the Palace defence before finding the bottom corner.

Palace did threaten another equaliser, but Dominic Calvert-Lewin converted from close range late on after Richarlison's headed attempt came back off the crossbar, wrapping up a fifth Premier League win in eight matches for Everton.