Two second-half goals from half-time substitute Fernando Forestieri in the space of 10 minutes saw the Hornets take the points after Michail Antonio's 19th-minute opener.
First Forestieri drove home Almen Abdi's corner in the 53rd minute and then he provided an emphatic finish just after the hour as Gianfranco Zola's men completed a turnaround.
With Hull losing at Crystal Palace, it allowed them to move into the automatic promotion places, and they are now unbeaten in seven games and hitting their form just at the right time.
For Wednesday, it could have been a different story had they not wasted a host of first-half chances. After leading through Antonio's ninth of the season, which came courtesy of a Jonathan Bond howler in Watford's net, the Hornets keeper then produced a string of fine saves to keep the visitors' lead at one.
They were made to pay after the break and back-to-back defeats for the Owls mean they are only three points above the drop zone.
The Hornets are unbeaten at Vicarage Road since January 1 and they hit the ground running, spurning a couple of early chances to break the deadlock through Troy Deeney and Matej Vydra, the latter hitting the post.
But Wednesday were the recipients of a huge error from Watford keeper Bond as he could not control a wayward backpass by Marco Cassetti and Antonio nipped in to roll home on 19 minutes.
Bond then kept out Miguel Llera's free-kick and then Jeremy Helan's drive, with Kieran Lee then hitting the rebound wide.
It was chances galore as both sides attacked, with Daniel Pudil testing Chris Kirkland and Joel Ekstrand blazing over for the hosts, while Bond again had to act smart to keep out Wickham and Danny Pugh efforts.
Boss Zola had seen enough and made two changes at half-time, bringing on Forestieri and Nathaniel Chalobah, and it paid dividends within eight minutes of the restart.
Abdi whipped in a corner, Cassetti flicked it on and Forestieri smashed into the roof of the net.
Then 10 minutes later, Deeney sent in a deep cross, the striker controlled perfectly and drove home into the bottom corner.
Wednesday poured forward in search of a leveller and Bond had one final save to make as he kept out a Leroy Lita header at the death.