Fernando Torres' first league goal since December confirmed third place and automatic Champions League qualification for Chelsea.
In Rafael Benitez's last game, the Europa League winners led after six minutes when Juan Mata swept in after Tim Howard saved from Demba Ba.
With David Moyes also in charge for the final time, Everton pulled level with Steven Naismith's neat finish.
But Torres thumped in from a Victor Moses knock-down to earn the win.
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-BBC