The Owls got on top in the first half against their sloppy opponents but were unable to make their dominance count, with Tom Lees coming closest to breaking the deadlock when his unmarked header grazed the post.
Watford, though, were much-improved after the interval and Wednesday were grateful for goalkeeper Cameron Dawson making excellent saves to deny Hornets substitute Stipe Perica and stand-in skipper Tom Cleverley.
Having started life back in the second tier with a win against Middlesbrough last week, Watford settled for a share of the spoils on Saturday while Wednesday, who overcame Cardiff in their Championship opener, are another point closer to wiping out their 12-point deduction imposed by the English Football League before the start of the campaign.
Both sides brought back their first-teamers after they were rested in their respective Carabao Cup games in midweek but injury continues to sideline Watford captain Troy Deeney, plus fellow forwards Andre Gray and Gerard Deulofeu.
Glenn Murray therefore came in for his first Watford start but the veteran found himself isolated in the early stages as the visitors repeatedly ran into trouble while attempting to play out from the back.
Murray stung the palms of Dawson, whose inability to hold on to the effort had no significance as Joao Pedro blazed the rebound over – although the Brazilian had already been flagged offside.
It was Watford's only sniff at goal in a first half which Wednesday ended strongly. Lees should have put them ahead but his free header from Izzy Brown's floated free-kick struck the outside of the post.
Wednesday's lack of a cutting edge seemed like it would come back to haunt them shortly after Murray had been replaced on the hour by Perica, who almost had an instant impact.
Wednesday's defence was unlocked by some fine interplay by Pedro and Nathaniel Chalobah, whose clever flick across goal was met by a diving header from Perica, only for Dawson to get down low to his left and parry away.
There was more urgency from Watford by this point with Wednesday now penned deep into their own half. Barry Bannan hauled down Domingos Quina on the edge of the box but Ken Sema wastefully blazed over the resulting free-kick.
In the final 15 minutes, Dawson was called on again to make another fine save, once again diving to his left and palming away after Cleverley had broken into the box before curling towards the top corner.
Christian Kabasele's stretched finish looped over the bar following a final touch from a Wednesday defender and the hosts could have nicked it at the death but an unmarked Brown directed a header harmlessly wide from 10 yards out.