The decisive moment of the game came in the first half when Connor Wickham capitalised on being fouled by Nyron Nosworthy to blast the resulting free-kick past Jonathan Bond from 20 yards.
The 1-0 defeat made it nine games without a win for the Hornets, who have now also failed to score in their last four matches at home.
Watford spurned a good opportunity to take an early lead when a Sean Murray corner picked out Marco Cassetti but the unmarked defender could not direct his header underneath the crossbar.
The hosts had another opening when Nosworthy's ball forward from halfway picked out the run of Ikechi Anya but, after side-stepping Roger Johnson on the edge of the area, the Scottish international was unable to hit the target with his right-footed shot.
The Hornets had gone into the game on the back of four straight home defeats and their problems mounted further after 24 minutes when Wednesday took the lead.
Nosworthy was adjudged to have fouled Wickham around 20 yards from goal to the left of centre and the striker took the free-kick himself, blasting a right-footed shot past Bond to make the breakthrough.
It could have got worst for the hosts within five minutes when a mix-up allowed Jacques Maghoma to break clean through on goal, but Nosworthy made a last-ditch challenge from behind and referee Philip Gibbs adjudged him to have won the ball fairly.
The Hornets thought they were level five minutes before the interval when Anya got in around the back of the Owls defence to convert a Troy Deeny pass but it was ruled out for offside.
The hosts went close again in the last minute of the opening period when Damian Martinez failed to hold on to a Murray shot from the edge of the area but Anya could not get enough power and direction to beat the Wednesday keeper from his follow-up.
The second half followed much the same pattern as the first, with Watford having the majority of possession and the Owls content to get numbers behind the ball.
Unlike the opening period, though, the home side found it even harder to create chances and their approach play became increasingly desperate.
Hornets manager Gianfranco Zola tried to do what he could to change things around, bringing on the more attack-minded Diego Fabbrini, Fernando Forestieri and Lewis McGugan at various stages after the interval, but they were still unable to force Martinez into a save.
It looked like that might change with six minutes remaining when Murray took aim from distance, and although his right-footed strike was blocked, it broke for Fabbrini in the area but his blushes at putting a good chance over the top were spared by the linesman's flag.
Watford's afternoon was summed up in the last of five minutes of injury time when Fabbrini slipped in Forestieri but, with only Martinez to beat from six yards out, he stabbed the ball wide of the target.