Everton began strongly in the south-coast sunshine with Richarlison thumping the woodwork with a dipping drive.
Wilson nodded the hosts into the lead from a corner in the 23rd minute only for Dominic Calvert-Lewin to level it up with a header just before the break.
It was Everton’s first away goal in the league this season. But Ryan Fraser’s dangerous ball into the area flicked off Everton’s Fabian Delph in the 67th minute to restore Bournemouth’s lead.
And Wilson exploited some dreadful defending five minutes later to earn Bournemouth their first home win of the season.
Everton, who could have gone third with a win, are now 11th, below Bournemouth on goal difference with both clubs having seven points from five games.