The veteran striker gave the home side a two-goal interval lead then completed his hat-trick five minutes after the break when goalkeeper Paul Jones was completely deceived by the bounce of a harmless through ball.
Stewart received rapturous applause from the crowd when replaced by Chris Brown in the 66th minute and the substitute helped a Steve Caldwell header over the line in the 73rd minute to give the home side a commanding four-goal lead.
But substitute Bruce Dyer, a 70th minute replacement for a subdued Heider Helguson, reduced the deficit in the 76th minute and three minutes into injury time was again on hand to beat goalkeeper Thomas Myhre from close range.
Leading scorer Stephen Elliott played a big part in the opening goal, latching on to a header from Carl Robinson and crossing for Stewart to nod home at the far post.
Stewart's second goal came via the penalty spot after James Chambers brought down George McCartney as the Northern Ireland international broke into the area. Stewart calmly sent Jones the wrong way before dispatching the spot kick to the goalkeeper's left.
The home side had the ball in the net again in the 42nd minute, a sweetly struck volley by Julio Arca from Stewart's centre giving Jones no chance only for the effort to be ruled out for offside.
Watford finally responded on the stroke of half-time when Helguson climbed above Gary Breen only for Myhre to produce a fine diving save.
But the third goal proved to be decisive with Sunderland manager Mick McCarthy able to bring Stewart off and give youngster Brown more valuable experience in the end of season push for promotion.
Jones atoned for his blunder by making outstanding saves in the later stages from Brown and Elliott as Sunderland threatened to run riot.