Bournemouth should have been ahead inside the first 10 minutes, although Benik Afobe saw his effort somehow flicked over the bar by Miguel Britos from just five yards out, after profiting from Ryan Fraser's initial shot.
The visitors had to call on Heurelho Gomes before the break, as Afobe held off his marker smartly only to see his shot from a tight angle saved down low by the Watford stopper.
The best chance of the half fell to new Watford frontman Andre Gray and he should have done a lot better, the striker somehow skying over the crossbar from six yards out after being picked out cleverly by Richarlison inside the box.
The Hornets should have again taken the lead in the early stages of the second half, only for Chalobah to make a mess of his effort despite finding himself one on one with Bournemouth stopper Asmir Begovic.
The goal that Watford's second-half dominance perhaps deserved came in the 73rd minute, as Richarlison capped off an impressive afternoon by poking beyond Begovic at the second time of asking to make it 1-0.
The Hornets capped off an impressive performance with four minutes of regular time to go, when substitute Capoue rifled home from 25 yards out in order to seal a 2-0 victory on the road.