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Connor Wickham's free kick midway through the first half proved sufficient in caretaker boss Stuart Gray notching the Owls' first win away from Hillsborough all season and condemn Gianfranco Zola's men to their fifth successive home defeat in the process.
The Hornets, who are yet to win in any of their previous nine fixtures, went behind on 24 minutes through Wickham, whose free kick sailed past Watford shot-stopper Jonathan Bond.
Martinez then produced a double-save in the closing stages of the opening half to ensure parity; first to deny Anya once more, before the Arsenal loanee replicated his heroics to keep out Sean Murray.
The visitors were left breathing a sigh of relief after the referee elected against pointing to the penalty spot, as Roger Johnson appeared to tangle with Marco Cassetti in the area in the closing stages.
Despite Zola's men pushing for an equaliser in the dying embers, the Owls held on for their first three points away from the Steel City all season.