Tonge struck with a spectacular left-foot drive early in the first half and Chris Porter sealed Watford's fate with his second goal in consecutive games.
Derby had a great chance to take the lead when Stephen Pearson surged into the box in the opening exchanges, teeing up Paul Green but his effort from 15 yards was pushed away by goalkeeper Scott Loach.
But Loach was beaten just four minutes later when Tonge finally ended his goal drought with a 25-yard shot that went in off the underside of the bar.
The hosts were in control but were given a reminder five minutes before half time that the game was far from over when Danny Graham got in front of Stephen Bywater and flicked a header just over.
The visitors had offered little as an attacking force in the first half but they went close to equalising in the 54th minute when Henri Lansbury's low drive forced Bywater into a sprawling save.
Lansbury had a great chance to level in the 70th minute when Dean Moxey's back header fell short but the midfielder delayed his shot which allowed Nicky Hunt to make a vital challenge.
It was a let-off for Derby, who were looking far from secure, but their nerves were settled in the 76th minute when Porter secured the win.
A mistake by Jay Demerit let Porter in and the striker showed good composure to fire low into the bottom right corner.
It was his second goal against Watford this season and this latest defeat means the Hornets have not won on the road since October 17th, a run of 11 Championship away games.