Kurt Zouma's first Everton goal, as well as a stoppage-time strike from substitute Dominic Calvert-Lewin, helped Everton secure all three points against a plucky Bournemouth side during a nervy affair at Goodison Park.
Zouma, on-loan from Chelsea, leaped above his marker in the box and made Asmir Begovic pay as the goalkeeper rushed off his line - only to be beaten with an emphatic header. Calvert-Lewin applied the finishing touch in stoppage-time, latching onto Ademola Lookman's clever pass before watching his deflected strike squeeze beyond a helpless Begovic.
While leapfrogging Eddie Howe's side and Wolves into 10th place, this result halts their four-match Premier League winless run at home, with their last win being against Cardiff in November.
Things might have been completely different if the visitors were able to capitalize after a bright start packed with half-chances. Joshua King and Junior Stanislas forced Jordan Pickford into important saves, while David Brooks hit the post after 15 minutes.
Cherries come close but to no avail
Brooks, the visitors' most lively player, had a penalty appeal waved away minutes earlier after tussling with Idrissa Gueye in the box.
Everton centre-back Michael Keane had a header hit the crossbar, while Nathaniel Clyne's important interception denied Lookman a chance to break the deadlock midway through the half.
The hosts' combination play and movement in the final third was promising - Lookman and Lucas Digne at the forefront - but their final ball was lacking. With that in mind, it was unsurprising to see Marco Silva's men return with more energy and impetus to begin the second-half.
Nathan Aké made a crucial goal-line block to deny Richarlison's goalbound effort just minutes after the restart, though the game's frenetic nature only intensified.
Everton take the lead and importantly, retain it
Zouma's headed finish was a timely one, coming on the hour mark at a time when Bournemouth were threatening on the counter-attack. His passionate celebration was telling: One appearance shy of his 100th in England's top-flight, it was only his third goal - all for different teams.
Joshua King squandered a one-on-one chance after Keane lost possession and committed a foul high up the pitch, with the Cherries' attacking threat still prominent as legs continued to tire. They had gained 26 points from losing positions since the start of last season - only Arsenal have more - so continued to press for a late equalizer.
Jordan Pickford made an important intervention to thwart Ryan Fraser as the Scotland international shaped to shoot, rushing out and clearing his lines with composure. Keane made a match-winning block to deny Dan Gosling as the midfielder aimed goalwards before Calvert-Lewin scored with virtually the last kick of the game with a deflected strike to put the icing on the cake during a hard-fought win.
Next up for Everton is an away trip to Southampton. Eddie Howe's side have now only won two of their last 12 league games and host an unpredictable West Ham next weekend.