Zuniga, a substitute in the 82nd minute, had been on the pitch for less than 60 seconds when he was picked out by Roberto Pereyra to restore Watford’s lead after Marcus Rashford had cancelled out Etienne Capoue’s first-half opener.
Deeney's stoppage-time penalty condemned Jose Mourinho, the United manager, to a third successive defeat in all competitions for only the third time in his career.
The Hornets took the lead on 34 minutes after Daryl Janmaat cut the ball back for Capoue to score his fourth goal of the season.
United were level on 62 minutes when Rashford finished from close range after combining with Zlatan Ibrahimovic, who almost put his side ahead, only to see his header superbly saved by Heurelho Gomes.
But it was Watford who struck late to seal the three points that take them up to eighth, two places behind the Red Devils.
Man of the Match: Sebastian Prodl