Watford held the early advantage in terms of territory although Stoke's strikers, Fuller and Mamady Sidibe, were a handful on the break.
It was the pace and trickery of Fuller that carried the biggest threat but neither keeper was seriously extended in the opening 25 minutes.
Stoke had half-hearted appeals for a penalty refused when Liam Lawrence went to ground under the challenge of Jobi McAnuff before Watford created the first two real opportunities of a hard-fought contest.
Marlon King seemed to be well-positioned to open the scoring from Jordan Stewart's 28th-minute cross, but he sliced his shot horribly and the ball trickled out for a throw-in.
King did fare better a minute later when he turned smartly on the edge of the penalty area before firing in a shot that Steve Simonsen turned away for a corner.
But a first half where endeavour comfortably over-shadowed quality, drew to a close with honours even in every respect.
Stoke attempted to up their tempo at the start of the second half and came close to taking the lead in the 33rd minute.
Fuller's full-blooded 12-yard shot was blocked on the line by Lee after Sidibe had picked out his strike partner.
Watford were not out of it and Tommy Smith dragged a shot only inches wide after a goalmouth scramble on the hour.
But Stoke continued to look the most likely side to snatch victory as a deflected effort from Richard Cresswell was pawed away for a corner by Lee before Fuller's late chance.