Striker Deeney notched twice in two minutes at the start of the second half to take his season tally to 20 after Gabriele Angella and Lewis McGugan had set the Hornets on course for a first victory on the road since October 5.
Wednesday, without head coach Stuart Gray because he was attending his son's wedding, pulled one back through on-loan striker Benik Afobe but were well beaten.
Watford went ahead in the fifth minute with the game's first goalmouth action.
Midfielder Daniel Tozser's free-kick midway inside the Wednesday half was headed down by McGugan and partially saved by Owls goalkeeper Chris Kirkland before defender Angella tapped home the loose ball for his seventh goal of the season.
The home side responded and midfielder Liam Palmer saw his ninth-minute shot from the edge of the area tipped wide by Hornets keeper Manuel Almunia before full-back Lewis Buxton's effort from the resultant corner was deflected behind.
Winger Chris Maguire was the next to go close for Wednesday when his goal-bound shot following Joe Mattock's low delivery from a right-wing corner was blocked on the line by Italian Angella.
Midfielder McGugan extended the visitors' lead with 23 minutes played.
Wing-back Daniel Pudil raced away down the left before producing an accurate centre for McGugan to head his ninth goal of the campaign into the bottom-right corner past helpless keeper Kirkland.
Wednesday striker Afobe forced Almunia to beat away his low shot moments later as the hosts looked to halve the deficit.
Watford wrapped up the three points within five minutes of the restart thanks to Deeney's quick-fire double.
The striker calmly slotted the ball past Kirkland after being put clear by McGugan's through ball in the 49th minute before tapping home a minute later after Mathias Ranegie's close-range attempt came back off the left-hand upright.
Wednesday pulled one back in the 54th minute when youngster Afobe, on loan from Arsenal, powerfully headed Palmer's right-wing cross past Almunia for his second Owls goal.
Substitute striker Atdhe Nuhiu headed straight at Almunia as the home side looked for another goal back before a volley from Watford's Swedish forward Ranegie was caught by Kirkland at the other end.
Wednesday, who had won four successive home games ahead of kick-off, were denied a second with three minutes remaining when Oguchi Onyewu's looping header bounced back off the crossbar with Almunia beaten.
Owls midfielder Kieran Lee then saw his stoppage time attempt saved by Almunia as Watford won 4-1 at Hillsborough for the second successive season.