The Toffees have never left the Vitality Stadium victorious in the PL era, and a one-sided first half on the south coast indicated they would struggle to break their duck here too.
The Cherries have been a threat from dead ball situations of late, and that route of attack almost bore fruit inside 10 minutes when Dean Huijsen flicked a long throw onto Dango Ouattara, but the winger’s first-time shot was well saved by Jordan Pickford.
The England goalkeeper was beaten on the quarter-hour mark by Antoine Semenyo, but his sweeping strike from Ryan Christie’s cross was chalked off for offside.
Undeterred, Andoni Iraola’s men kept piling forward, with Evanilson flashing an effort wide before Justin Kluivert was played in on the inside right only for the onrushing Pickford to smother his attempted chip.
The Everton stopper held a header from Semenyo as half-time approached, with Sean Dyche’s toothless side blunted further by an early withdrawal for striker Armando Broja, who was again forced off injured.
Despite a double substitution at the break from the visitors, it was Bournemouth who continued to dominate proceedings, with Pickford making a pair of impressive saves to deny low drives from Semenyo and Ouattara.
Frustration was growing amongst the home faithful however, as chances began to dry up beyond the hour mark, leaving Pickford and centre-back duo James Tarkowski and Jarrad Branthwaite increasingly comfortable.
That changed in the 77th minute though, as a tremendous cross from flying full-back Milos Kerkez was met by a wonderfully controlled first-time volley from substitute David Brooks, whose strike nestled in the far corner after narrowly sailing over Branthwaite’s head.
The Welshman’s second goal of the season was enough to secure victory for the Cherries, who secured a double over Everton after producing a famous comeback to win the reverse fixture.
They stay in the top seven and amongst the European challengers as a result of a fifth successive home H2H win, while Everton sit just two points clear of the drop zone after failing to score in a fifth consecutive away match.