However, the inspiration behind the win was Robbie Blake. The former Leeds striker was given licence to roam behind Andy Gray and he tormented the Hornets defence all night, and in particular out-of-sorts left-back Jordan Stewart.
Blake should have been awarded a penalty late in the first half when he was clearly taken out by Jay DeMerit, having earlier curled in a free-kick which Chris McCann headed down and off Mart Poom's left-hand post, with the Hornets keeper beaten.
The closest the home side came to a breakthrough in the opening period was when a shocking Gabor Kiraly fell invitingly for Marlon King. Watford's joint top scorer had a clear shot on goal but blasted his shot too close to the keeper, who deflected the effort over.
Burnley maintained their positive approach after the break and were almost rewarded when Poom made a fine full-length save to keep out Gudjonsson's long-range effort.
Minutes later though, the Estonia international was beaten by Gray's close-range header after Wade Elliott had produced an excellent cross from the right.
The disappointing home side sought a way back, without really threatening, and they were undone again with ten minutes remaining when Blake's cute pass sent Gudjonsson racing clear from halfway and the substitute kept his head, rounding Poom to finish from a tight angle.
Dan Shittu's third goal in two games five minutes from time did give the Hornets hope, but a draw would have flattered a side who now look nothing like the runaway champions some were predicting a few weeks back.