It took 12 minutes for either side to have a pop at goal, when Blackburn's David Dunn's speculative volley soared well wide of the target.
The Rovers stopper pulled off a double save moments later, first stopping Deeney's header before keeping out Ikechi Anya from the rebound.
The Hornets again came close in the 37th minute, as Forestieri turned in the middle of the pitch, drove at the Rovers backline, before bending a shot just wide of the far post.
Watford went took the lead just seven minutes into the second half, when Deeney's low shot found the bottom corner of the net after wrong-footing Gael Givet.
Blackburn went in search of a leveller, and on the hour Jordan Rhodes rose but could only direct his header from Dunn's cross over the bar.
However, Watford doubled their advantage shortly after when Forestieri threaded through Deeney, who got behind Givet before slipping it past Sandomierski to add his and his side's second goal of the afternoon.
The Hornets added a third in the 68th minute, when Forestieri again turned the provider to loft a pass to Abdi, who turned and fired high into the net to make it 3-0.
The hosts added a fourth 13 minutes from time when Briggs slammed home after a corner had led to a goalmouth scramble.