It was a superb end to a great second-half that was end-to-end stuff after a poor opening period. Two tries in as many minutes from home full-back Martyn Thomas and replacement centre Lewis Robling against one from Ospreys wing Tommy Bowe had the crowd on their feet.
Dragons stand-off Jason Tovey booted 11 points, with Ospreys counterpart Matthew Morgan contributing five penalties for a 15 point haul.
The Dragons went into the break 9-6 ahead as Tovey, who had recovered from a miserable night against the Scarlets last week, landed three penalties against two from Morgan.
But the game by then was only noteworthy for three yellow cards dished out by referee James Jones — for Ospreys forwards Ian Evans and Tom Smith, plus home wing Tonderai Chavhanga — than for any threats on the try-line.
However, where the first-half was a squib, the second period was pulsating. Barry Davies was just short with an ambitious 48-metre drop-goal before Morganlevelled the game with a penalty. But a double strike from the home side took them clear. A great multi-handed move that criss-crossed the pitch finished with full-back Thomas cutting inside to beat three defenders for the try.
Two minutes later, Morgan threw an innocuous pass to his centres only for Robling to intercept and race 48 metres under the posts, with Tovey converting. It put the Dragons 21-9 ahead and in the driving seat. But the Ospreys dug in and gave themselves a chance of taking the honours at the death.
Morgan added two penalties and, with 16 minutes still to go, the visitors were back within a converted try of victory.
And they grabbed a thumping score which involved centres Tom Isaacs and Beck to set Irish wing Tommy Bowe in at the corner. However, the Dragons could have had very valid arguments for two forward passes in the movement. Biggar missed the crucial conversion from wide out.
It all boiled down to Biggar’s attempt at a grand finale, but his well struck drop goal effort cam back off the upright.
DRAGONS: M Thomas; W Harries; A Brew, A Smith, T Chavhanga; J Tovey, W Evans; N Williams, S Jones, N Buck, A Jones, R Sidoli, D Lydiate (capt), L Evans, T Faletau.
Replacements: L Robling for A Smith (22), M Jones for Tovey (75), J Bedford for W Evans (77), R Buckley for S Jones (64), D Way for Buck (66), J Groves for A Jones (79), D Waters for L Evans (72).
OSPREYS: B Davies; E Walker; T Isaacs, A Beck, H Dirksen; M Morgan, R Webb; D Jones, H Bennett, A Jarvis, R Jones, I Evans, T Smith, J Tipuric (capt), J Bearman.
Replacements: T Bowe for E. Walker (70), D Biggar for Morgan (61), K Fotuali’i for Webb (55), P James for D Jones (50), R Hibbard for Bennett (50), A Jones for Jarvis (50), J Thomas for Evans (43), G Stowers for Bearman (58).
Referee: James Jones (WRU).