A goal in each half by Grabban and Harry Arter, prior to Brett Pitman's late penalty, earned the Cherries a 12th win in a remarkable run of 14 unbeaten matches.
Grabban's fine goalscoring form has been a major factor in Bournemouth's success since manager Eddie Howe returned to the south-coast club.
The striker gave Bournemouth a 32nd-minute lead. Grabban troubled the Yeovil defence with his pace throughout and his clinical move on the left with Marc Pugh set up a richly-deserved ninth goal of the season.
Stretching Yeovil on the flanks, Bournemouth had several opportunities to improve on Grabban's first-half goal before Arter doubled the lead when he drilled a fierce 73rd-minute left-footed shot into Marek Stech's top corner.
Yeovil had their chances, notably efforts from Jamie McAllister and a header from Dominic Blizzard, which looped just over the crossbar, before Pitman wrapped things up from the penalty spot.
Luke Ayling handled and Pitman made it 3-0 from the penalty spot for his first Cherries goal since his return from Bristol City.