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Gianfranco Zola's promotion hopefuls had several opportunities to break the deadlock before Deeney's opener.
The on-loan Stoke City stopper saved his first-time drive moments after denying Almen Abdi from Vydra's cutback.
Watford were frustrated again when another Vydra effort was deflected over the crossbar by Curtis Davies, but their persistence paid off on 38 minutes.
Deeney, who had earlier headed narrowly over the crossbar from a good position, made amends by nodding Anya's cross into the net from six yards.
Anya soon added his own name to the scoresheet when he capitalised on poor Birmingham defending to strike low past Butland at the near post.