Almen Abdi broke the deadlock with a free-kick before Deeney helped himself to a first-half brace, his first of the game coming from the penalty spot after goalkeeper Marcus Bettinelli brought down Matej Vydra to earn a straight red card.
A superb second from Abdi six minutes into the second half piled on the misery for Fulham before Deeney struck with virtually the final kick to take his tally for the Championship season to seven as Watford cruised to an emphatic victory that leaves them sixth.
Slavisa Jokanovic's men were dominant from the off as Daniel Tozser's rasping set-piece brought a fine one-handed save from Bettinelli.
Tozser continued to be in the thick of the action as his punted clearance caught the Fulham defence cold and allowed Deeney to steer a header past the advancing Bettinelli, but Kostas Stafylidis scrambled back to frantically hack clear on the line.
However, all Watford's early pressure reaped reward in the 15th minute when Abdi drilled a free-kick on the edge of the penalty area low through the wall and into the net.
Then came Bettinelli's dismissal as he was unable to cope with Vydra's pace and sharp footwork. Deeney sent replacement goalkeeper Gabor Kiraly the wrong way from the resulting spot-kick.
Deeney was again on target 10 minutes before half-time from close range and Abdi followed suit in getting his name on the scoresheet for a second time after the restart.
And, in the 93rd minute, Deeney put the seal on an impressive individual and team performance when he timed his run to perfection and scampered clear before rifling past Kiraly.
