Dean Moxey's Bolton career almost began in calamitous circumstances as his first touch of the season was an underhit backpass, and although Deeney intercepted he fired his near-post shot into the side-netting.
However, the home side dominated proceedings and Deeney's 17th-minute opener was well deserved. Gabriele Angella rampaged down the right flank before picking out his forward, who lifted a clever finish over the advancing Andy Lonergan.
Deeney's strike partner Vydra doubled the lead just six minutes later when he raced away and slotted a finish beyond the reach of Lonergan.
Almen Abdi twice came close as the game approached half time, while Deeney also threatened once more, but Watford went into the break 2-0 ahead.
The second half picked up where the first had finished, with Watford in the ascendancy, and Abdi saw his deflected strike bobble just wide of the post in the 56th minute.
Substitute Jermaine Beckford then cut inside and thrashed a shot into the side netting as Bolton looked for a late comeback, but any hopes were extinguished with 10 minutes left to play when Fernando Forestieri pounced on a defensive mistake to make it 3-0.
There was still time for Gomes to make an extraordinary save late on from Lee's header to round off a superb afternoon for the hosts.