No.8 Scott Hicks bagged a first-half try fror the Ospreys with centre Kristian Phillips adding a conversion and penalty.
Ryan Bayliss crossed for a second try after the interval, before limping off with a hamstring injury, whilst fullback Chris Lewis suffered the same injury and played for just 90 seconds of the contest.
Wing Matthew Pewtner struck for the Dragons in the second half with Tom James adding a brace of penalties. The home region had their chances and were camped on the Ospreys line when the game came to a close.
Dragons Team Manager Billy Vyvian commented, "It was a game that swung to and fro either side of half time. We started well but trailed 10-0 at half time. After that, they bagged a second try before we finished with 11 points.
"I think we can be proud of this performance and happy with the manner in which we approached a very difficult game against a very good side."
Ospreys High Performance Manager Dai Arthur said, "This competition is all about producing good players, but if we can win all of our games along the way, then so be it.
"Our aim each season is to make the three finals and this result means we are almost certain to make the U18 final once again."
In the other game, the Blues defeated the Scarlets 34-17 to improve their chances of reaching the final.
James Loxton, Dean Gunter, Garrick Legge, Gareth Capelin and Gus Davies crossed for tries as the Blues bagged a bonus point before half time.
Outside half Ian Smerdon kicked a penalty and three conversions whilst for the Scarlets scrum half Gareth Davies and centre Scott Williams scored tries with Daniel Etteridge adding two conversions and a penalty.
Blues High Performance Manager Gafyn Cooper said, "We were 10-0 down quite early on, but fought back well and picked up a bonus point by half time.
"The win puts us in with a good chance of reaching the final, but we will need to win our remaining games."