Goals from Philip Billing, Dango Outtara and Daniel Adu-Adjei secured a decisive victory for Andoni Iraola's Bournemouth team in a match played under intense heat.
Following a subdued first half, Billing struck Bournemouth ahead in the 55th minute, evading his defender at the edge of the box before launching a powerful shot that zipped past Everton goalkeeper Jordan Pickford.
England international Pickford was beaten again just four minutes later after a play that started when Outtara broke free down the left side.
Everton defender Nathan Patterson seemed to have dealt with the threat, but a misjudged touch allowed Burkina Faso international Outtara to strike a shot high into the net past Pickford's near post.
Adu-Adjei made it 3-0 for the Cherries in the 69th minute, capitalizing on a weak backpass from Jake O'Brien to finish calmly past Pickford.