Vydra's superb strike sent the Hornets into half-time ahead and Joel Ekstrand netted to double the lead midway through the second half.
Jamie Ward soon reduced Derby's deficit to a single goal again from the penalty spot.
The Rams pushed for an equaliser but could not significantly test teenage goalkeeper Jonathan Bond, who was making his first league appearance for Gianfranco Zola's side after Manuel Almunia went off injured at the end of the first half.
Derby had some defending to do early on and should have been behind after five minutes.
Vydra was denied by goalkeeper Adam Legzdins when clear through on goal, the rebound fell into the path of Geijo but he volleyed over the crossbar.
Derby looked dangerous on the break. Ward sent a shot over the bar and Conor Sammon headed wide as the quarter-hour mark arrived.
However, two minutes later Watford were in front. Vydra's shot from the left side of the area flew past Legzdins, striking the inside of the far post before trickling into the back of the net.
The Rams will have been keen to test Bond but it was Legzdins who was busier, blocking at his near post to deny Almen Abdi 10 minutes after the restart.
Ekstrand made it 2-0 in the 68th minute when he met Abdi's inswinging corner 10 yards out and steered a right-footed shot past Legzdins.
However, Derby were handed a lifeline five minutes later when Lloyd Doyley pushed over Ward. The Northern Ireland international picked himself up and, in front of the 929 travelling supporters, struck his spot-kick straight down the middle of the goal.
The Rams sensed they could get something from the game and Bond had to save efforts from substitute Mason Bennett and Martin, while Ward saw a shot clear the bar.
However, Watford held on for a seventh victory in the last nine league games and went second in the table behind leaders Cardiff.