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After a dominant spell of possession for the Hornets, Charlton started to find their way into the match, and were able to take the lead when Callum Harriott drilled the ball in from just outside the box.
The hosts had the majority of the possession at the start of the second half, but could not prevent the visitors from getting back on level terms with half an hour still to play, with Hamer unable to stop a 25-yard strike from Deeney.
The striker, who now has 24 goals this season, tried to claim his second of the evening shortly after, but his finish from close range comfortably cleared the bar.
The hosts punished Watford for the miss just moments later, as Johnnie Jackson tapped in from close range at the other end less than a minute after Deeney's miss to put Charlton back in front.
Charlton extended their lead a few minutes later when Harriott converted from close range for his second goal of the evening.
Watford's hopes for a comeback were dealt a blow when Albert Riera picked up his second booking, leaving the visitors a man short for the final 12 minutes.
Charlton had chances to extend their lead further, but had already done enough to make sure of the three points, which leaves them five points clear of the relegation zone with just one game still to play.