Richarlison was the hero again, scoring for the fourth straight match, as Everton’s third successive win took them up to fifth place.
West Bromwich Albion caused the Toffees early problems, with Mbaye Diagne’s header forcing a flying save from Jordan Pickford.
But Everton gradually found their feet and twice went close before half-time. Richarlison’s shot was deflected over the bar and Dominic Calvert-Lewin fired straight at Sam Johnstone from a good position.
The decisive moment came in the 65th minute as Gylfi Sigurdsson crossed from the left side and Richarlison headed home inside the six-yard box.
Diagne fired home at the other end late on, but his strike was ruled out for offside.
Carlo Ancelotti’s side jump two places and sit one point outside the top four, with a match in hand on all of the sides above them.
West Brom remain 19th, nine points from safety.