It was replacement prop Luke Yendle who got the ball down under the posts, with 13-point flyhalf Lloyd Evans landing the resulting kick to snatch the spoils.
Dragons Delighted head coach Dai Flanagan commented: "I thought the character to pull it back was excellent and it's something we can really build on.
"I am just really proud of the problem solving and us having clarity in what we were doing. That is real maturity from us. We spoke in the week about going 12 rounds. I might have to change that to six rounds because I don't think I can go through that again!"
Amid an early exchange of penalties between fly-halves Evans and Dan Edwards, it was the home side who had the better of the opening quarter in terms of territory and possession.
But then, in the 20th minute, the Ospreys carved out a well worked converted try.
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