Albion lead through a Neal Maupay goal scored just before half time as the Seagulls striker turned home a Tariq Lamptey cross.
Maupay had an earlier chance that was beaten away by the former England keeper Ben Foster.
Jakub Moder also went close after good work by Pascal Gross.
At the other end, Watford have pressed Albion and Lewis Dunk received a yellow card.
Foster also cleared the ball straight to Lamptey but he was unable to take advantage.
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