The contest looked to be an even affair in the opening stages but the hosts found their first goal after 15 minutes.
Almen Abdi had Watford's only real chance of the first period in the 30th minute but the midfielder's effort from outside the area rolled wide of the target.
The hosts managed to score two more times before the interval, with Jeff Hendrick finding space to head in from close range before Sammon added another on the stroke of half time.
Sammon's finish was the highlight of the game, with the striker being put through on goal before lobbing Manuel Almunia from outside the area.
Keogh was close to grabbing a brace before the break but his shot crashed against the crossbar and the hosts had to settle for three goals in the first period.
Derby's superiority continued in the second half and they had their fourth goal of the game in the 52nd minute.
A free kick from Ward was well saved by Almunia but Will Hughes reacted quickly to score his first ever goal for Derby and to effectively put the result beyond doubt.
Derby continued to attack and Ward finally got the goal that his performance deserved as he collected a pass from Paul Coutts before slotting past a despairing Almunia.
Matej Vydra did manage to find a consolation goal for Watford from close range but the hosts were rarely troubled again to finish as comfortable winners.