The result continued the Ospreys’ remarkable winning record against their Welsh rivals – taking their unbeaten run to 15 games.
A score from Tom Habberfield and a penalty try cemented the Ospreys’ place in the new Rugby Champions Cup next season as they moved 14 points clear of West Wales rivals Scarlets in the PRO12 standings.
Richie Rees had given the Dragons hope of snatching a remarkable victory, but Steve Tandy’s men wrestled the advantage from the Men of Gwent in the second half.
Richard Fussell thought he’d scored against his former side after five minutes. Referee Nigel Owens originally gave the try, but decided that Ospreys scrum-half Tom Habberfield had knocked on in build-up after consulting the big-screen.
Promising No 8 Dan Baker was the second player to cross the Dragons try-line without scoring. Strong drives from Jeff Hassler and Justin Tipuric set up Baker to crash over, but he lost control of the ball as he attempted to touch down.
It was somehow still 0-0 after half-and-hour, the Dragons had to repel attack after attack from the likes of Alun Wyn Jones and the elusive Hanno Dirksen.
But they received a huge boost with their first forage into Ospreys territory. Bristol-bound Ryan Jones was shown a yellow card for slowing the ball down illegally five metres from his own line.
The deadlock was finally broken after 46 minutes when Rees scored the most unlikely of tries. After a half of Ospreys dominance, Tyler Morgan, making his PRO12 debut, stepped past the tackle of Spratt and offloaded to Cory Hill, who released the ball to former Cardiff Blue Rees – who darted across the line, giving Kris Burton the easiest of conversions.
Nic Cudd was the second man to be sent to the sin-bin by Nigel Owens after he infringed at a ruck. Dan Biggar knocked over the resulting penalty to claw the Ospreys back into within four points.
The Ospreys took the lead through scrum-half Habberfield after 60 minutes. The 21-year-old finally broke the Dragons brick-wall defence after a series of pick-and-go efforts weakened their resolve.
Tom Prydie levelled the match with a penalty against his former side, after Jonathan Spratt was yellow carded for a deliberate knock-on during a promising Dragons attack.
Biggar restored the lead for Steve Tandy’s men before the Ospreys pack demolished the Dragons scrum to win a penalty-try and seal the victory.