This win came just days after Everton chief executive Denise Barrett-Baxendale set a target of winning the Premier League and playing Champions League football at the club's new stadium during the next decade.
After Kurt Zouma opened the scoring for Marco Silva's men in the 61st minute, Dominic Calvert-Lewin then sealed the victory in stoppage time with Lookman providing the assist to end any hope of a comeback from Eddie Howe's side. "We have to achieve the results, for us it's important to regain some form, and some confidence also and a clean sheet is also important".More news: Samsung Galaxy M series will compete with Redmi and Realme
"It was difficult at the end because they were pushing hard and they tried to put the ball in our box and play the second ball so we stayed compact and I think we did really well".
And it was the visitors who started the brighter but, with the injured Callum Wilson missing, Bournemouth were unable to capitalise despite creating the better chances.
The result sees Everton move up to 10th in the Premier League table, while Bournemouth remain in 12th.More news: Carlos Ghosn seeks bail after 2 new charges
On the hour mark, Kurt Zouma finally grabbed the lead for Everton, when the defender headed home from Lucas Digne's cross at near post, 1-0.
Keane and Pickford combined to deny Dan Gosling an equaliser and Calvert-Lewin - who replaced Richarlison - turned Ademola Lookman's cutback home in the 95th minute to guarantee the win.
It was the 24-year-old French centre-back's first goal since he scored for Stoke in a 2-2 draw with Brighton in November 2017. It was a bad performance for sure, but in some moments I can have a bad performance. Howe said: 'We're very keen to show a response to the recent run that we've been on'.More news: Wife of furloughed federal worker wins new SUV, $100K through lottery promotion