The Welsh Region had trailed 10-0 early on but responded emphatically with five tries, two from Wales second-row Andrew Coombs.
Centre Ashley Smith, hooker Rhys Thomas and flanker James Thomas also got over the line for the Dragons as they kept the pressure on Newcastle in Pool 3 of the Challenge Cup.
"That was a very pleasing performance," said Dragons head coach Jones. "The start did not go to plan but we kept our composure in difficult conditions, it was minus two when we kicked off, and ended up dominating.
"That will have been an excellent experience for some of our younger guys, to come to a hostile place, find themselves in trouble and work their way out of it.
"I also thought some of our older heads performed particularly well too. Richie Rees ran the game well for us at scrum-half, Andrew Coombs got through a lot of work alongside Cory Hill in the second row and the back-row also went well.
"That was the perfect outcome for us and we want to back that up when we face Bucharest again next week."
