Callum Wilson scored once in each half for the Cherries at the Vitality Stadium, with substitute Ryan Fraser also on target for the home side, and Howe was delighted to pick up a big three points.
Everton created several chances with Richarlison hitting the crossbar while Bournemouth goalkeeper Aaron Ramsdale saved efforts from Calvert-Lewin, Gylfi Sigurdsson and Alex Iwobi.
After not taking their opportunities, the Toffees came unstuck in defence with Wilson scoring from close range in the 23rd minute after Diego Rico's corner.
Fraser made it 2-1 with 67 on the clock - after Calvert-Lewin headed an equaliser a minute before the break - when his low free kick took a deflection off Fabian Delph and evaded Jordan Pickford.
The unmarked Wilson then wrapped up a bad day for Everton when he latched onto Rico's forward pass and lobbed home for his third goal of the season.
"I'm really, really pleased. You don't want to go too long without winning at home. This league is hard enough, but you are reliant on your home form," Howe said.
"We have been unfortunate in the previous home games because against Man City we played OK and Sheffield United scored in the dying minutes. We knew the importance of the game and it's a great win against a good team."
Howe heaped praise on Fraser too, who was dropped to the bench, but responded with a goal 10 minutes after his introduction.
"It was a moment in the game where it was 1-1, we hadn't started the second half particularly well and we really felt we needed his enthusiasm, his energy and quality. When he came on he made a huge difference," the Cherries boss said.