The Republic of Ireland Under-21 international broke the deadlock in the 18th minute when he sliced open the home side's defence before scoring with an angled shot from 12 yards.
He then delivered the corner kick which allowed Gabrielle Angella a routine header to double the Hornets' lead on the half-hour.
Murray claimed his second goal of the night five minutes later, smashing home a first-time shot from 15 yards after Javier Acuna had set up the chance.
The League Two club - who had hit the post through David Clarkson's deflected shot just before Watford's opener - did manage to pull a goal back five minutes before the interval.
Watford failed to clear a corner and Eliot Richards swivelled to convert after the ball had been headed back into the danger area by Tom Lockyer.