The visitors made a perfect start to the match when they took the lead after just four minutes. Sean Murray's long-range effort deflected off the head of Stephen Ward and past a helpless Thomas Kuszczak.
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Buckley again supplied the cross for Brighton's next chance, but this time Craig Conway could not steer his header on target with Almunia stranded.
Buckley continued to threaten and almost set up an equaliser right on the stroke of half time when his cross was hacked off the line by Joel Ekstrand with Barnes lurking close by.
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There was a moment of huge controversy at the start of the second half as Fernando Forestieri raced onto a Davide Faraoni through ball before slotting his effort past Kuszczak. Gordon Greer got back to stop the ball and the referee allowed play to continue, although replays suggested that it had indeed crept over the line.
Watford's outrage was exacerbated less than 10 minutes later as Andrew Crofts levelled things up for the hosts with a volleyed finish after the Hornets had failed to clear a Conway corner.
The visitors came within inches of regaining the lead with just five minutes left as Faraoni linked up with Forestieri once again, but this time the Italian's effort bounced back off the inside of the post.
Almunia was called into action moments later at the other end, but the Spaniard was equal to Barnes's well-struck volley.
Neither side could find a winner in the closing stages as the spoils were shared on a controversial evening of Championship football.