The Toffees have struggled at Goodison Park this season but were offered a huge gift to get going on this occasion. Just eight minutes in, Illya Zabarnyi slipped on the ball and rolled it across to James Garner, who capitalised on the centre-back’s error by coolly slotting home his first-ever PL goal.
Bournemouth’s shakiness continued with poor passes from Neto and Marcos Senesi being intercepted in dangerous areas inside the opening quarter-hour, but they ultimately went unpunished.
Bournemouth finally offered some promising signs as the half-hour mark approached, but their deficit was doubled soon after Dango Ouattara sent his strike harmlessly over the crossbar.
When Neto punched Vitaliy Mykolenko’s shot away, the ball fell invitingly for Jack Harrison who sent a wonderful strike in off the crossbar for a memorable goal on his first PL start for the Toffees.
Things could have got even better for Sean Dyche before the break with Dominic Calvert-Lewin hitting the crossbar and Amadou Onana’s effort whistling agonisingly wide.
Zabarnyi conceded possession cheaply again after the restart, but there was relief for the Ukrainian this time as Abdoulaye Doucouré rolled his shot straight at Neto.
The confidence was still flowing for Everton, as encapsulated by a superb touch from Calvert-Lewin and an audacious attempt, even if his shot sailed over the crossbar.
They got a deserved third mere moments later, with Doucouré reacting quickest when Milos Kerkez blocked Harrison’s header to dispatch the third goal in the midfielder’s last five PL matches.
Calvert-Lewin couldn’t quite get in on the goalscoring act with his dink going over Neto’s shoulder before eventually trickling wide.
There was still plenty of reason for Everton celebration, though, as the Toffees responded to their disappointing defeat against Luton Town by convincingly securing the third win in their last four across all competitions.
Bournemouth, meanwhile, continued the PL’s longest current winless streak having endured 12 league matches without tasting victory.
Flashscore Man of the Match: Jack Harrison (Everton)