Ospreys' director of coaching Scott Johnson was in Biarritz on a scouting mission ahead of the mammoth Heineken Cup quarter-final tie in less than two weeks and so missed his side's second league game on the trot without any points.
At a pumped-up Rodney Parade, his side struggled to cope as the Dragons raced into a quick-fire, 11-point lead inside as many minutes.
Tovey booted two penalty goals and claimed the assist for Will Harries' seventh minute try after an excellent chip to the right corner allowed the wing to beat Nikki Walker to the bounce of the ball.
The star-studded Ospreys were clearly rattled despite having 15 international stars in their ranks, but Biggar then got the visitors on the scoreboard with a close-range penalty.
They grew in confidence and after Jonathan Thomas, Jerry Collins and Lee Byrne were foiled short of the line, scrum-half Mike Phillips fed James Hook to crash over in the corner for a try which Biggar converted..
But the Dragons roared into the interval after Tovey added his third penalty and then centre Watkins produced a moment of magic on the stroke of half time to score a superb touch down from 40 metres.
The former Wales player sliced through a gaping hole in midfield before turning on the gas and then sidestep Tommy Bowe for a wonderful try.
The second period started calmly and Biggar briefly drew the Ospreys to within eight points with his second penalty before Aled Brew claimed a third Dragons try under the posts.
Andrew Bishop crossed for a late consolation for the visitors but the damage had been done.
Scorers: Dragons - Tries: Will Harries, Matthew Watkins, Aled Brew; Cons: Jason Tovey 2; Pens: Jason Tovey 3;
Ospreys - Tries: James Hook, Andrew Bishop; Cons: Dan Biggar, James Hook; Pens: Dan Biggar 2