Marc Pugh had an early attempt but his shot went high over the bar from 35 yards.
Watford took the lead through Gabriele Angella when the defender smashed the ball into the roof of net after Bournemouth failed to clear a corner.
However, despite more pressure from the home side, the Cherries came back into the game and equalised on 31 minutes through Grabban's third league goal of the season.
Ryan Fraser drove the ball into the box and Grabban duly slotted home into an empty net.
That goal gave Eddie Howe's men renewed confidence and they started to pressurise their opponents. However, they couldn't find a second goal before the half-time whistle.