The striker headed home his first goal from a fine cross by the lively Stephen Elliott in the 19th minute.
He converted a George McCartney-won penalty and then poached a third before Chris Brown fired in Steve Caldwell's knock-down for Sunderland's fourth.
Two late consolation strikes by Bruce Dyer flattered Watford, who were generally outplayed by their hosts.
Watford boss Ray Lewington:
"We never got going, the first three goals were all down to us. If you give goals away like we did it's hard to get back.
"You come to these big clubs and you know you're going to get beaten - we know it's going to be tough in games like these.
"It wasn't a very good display. We've got to get more discipline and consistency in our play."
Sunderland: Myhre, Wright, Breen, Caldwell, McCartney, Whitehead, Robinson, Whitley, Arca, Elliott, Stewart (Brown 67). Subs Not Used: Alnwick, Welsh, Thornton, Danny Collins.
Goals: Stewart 18, 33 pen, 51, Brown 73.
Watford: Jones, Darlington, Demerit, Cox, Doyley (Eagles 54), Ardley (Young 84), Jackson, Mahon, Chambers, Webber, Helguson (Dyer 70). Subs Not Used: Chamberlain, Blizzard.
Booked: Jackson.
Goals: Dyer 76, 90.
Att: 24,948
Ref: T Bates (Staffordshire).