Three down at halftime, Bournemouth, without a win in 2017, improved dramatically in the second half, Josh King reducing the deficit just before the hour after fine work from Jack Wilshere and adding another 10 minutes later with a sharp finish.
Yet the hungry Lukaku struck twice more in the final 10 minutes to take his season's league tally to 16, making him the top-flight's leading marksman as Ronald Koeman celebrated his 100th Premier League match as a manager.
Bournemouth's Harry Arter made it 5-3 in the 90th minute but Everton had the final word when Ross Barkley tapped home the ninth goal of the afternoon four minutes into stoppage time.
(Reporting by Ian Chadband; Editing by Brian Homewood)
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