Murray broke the deadlock after just four minutes when his long-range strike deflected off the head of Stephen Ward and past Thomas Kuszczak.
Lewis McGugan almost doubled Watford's lead five minutes later when he curled a shot just past the post from the left side of the penalty area.
Manuel Almunia was called into action for the first time in the 14th minute, getting a strong hand to Ashley Barnes's powerful header at the back post.
Almunia found himself helpless shortly afterwards, however, as Will Buckley's cross left the Spaniard stranded, only for Craig Conway to nod the ball just wide.
The hosts came even closer to restoring parity right on the stroke of half time when Buckley fired the ball across goal towards Barnes, but Joel Ekstrand hacked the ball off the line before it could reach the Brighton man.