After a tight opening 45 minutes, the Hornets produced an emphatic second-half performance to maintain their 100% start to the season.
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.
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However, despite more pressure from the home side, the Cherries came back into the game and equalised on 31 minutes through Lewis 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 Howe's men renewed confidence and they started to pressurise their opponents. However, they could not find a second goal before the half-time whistle.
The second half started at a rapid pace and Watford raced into a 3-1 lead with two goals in as many minutes.
Angella escaped the attention of the Bournemouth defence to score his second direct from an Almen Abdi free kick, but worse was to come for Howe's players.
Deeney linked up nicely with Fernando Forestieri and saw his shot take a slight deflection on its way in.
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The Cherries were lagging at this point and it was soon 4-1. Former Nottingham Forest player Lewis McGugan picked up Abdi's through-ball and placed it into the left-hand corner.
However, the best was yet to come via Deeney's second of the afternoon. The striker picked up the ball on the edge of the area and smashed it into the top corner.
His third goal came soon after from the penalty spot. Diego Fabbrini was tripped and Deeney made no mistake from 12 yards to add gloss to a comprehensive win.