Jack Grealish’s late winner saw Everton end Bournemouth’s unbeaten home record in the Premier League.
The Toffees faced it for long periods but found the edge when it came to going five games without a win for the hosts.
The Cherries have slipped to 14th in a congested intermediate table after an excellent start, while Everton are now ninth.
Antoine Semenyo had the best chance of the first half but was denied by a good save from Jordan Pickford after bringing home a deep cross.
Everton striker Thierno Barry headed against the woodwork as his wait for a goal continues before the visitors score a goal.
Grealish led a counter-attack, had space to cut inside and hit a shot which deflected off Bafode Diakite.
Only Arsenal have taken more points on the road since David Moyes returned to the club and Everton have held on to three more.
That makes it three wins from four for Everton, who host Nottingham Forest on Saturday.
