The Dragons had tries from Phil Price, Jason Tovey, Lewis Evans and Ashley Smith as they turned around with a 22-10 advantage.
A penalty from Tovey and try from Andrew Coombs put 20 points between the sides, with half-an-hour remaining. Edinburgh hit back with tries from Tim Visser and Geoff Cross, but they fell agonisingly short of claiming a losing bonus point.
The game marked Edinburgh's first outing since Rob Moffat was let go recently as head coach. Interim boss Nick Scrivener has taken over and the Scots stung their hosts with a third minute try.
John Houston and Ben Cairns got involved in midfield before danger man Visser was put into space on his wing. He chipped ahead and fellow winger Lee Jones raced through to react the ball first and get the touchdown.
Chris Paterson landed the conversion for good measure, before the Dragons used a solid lineout to attack from.
Wayne Evans shifted the ball at pace, back and forth across the pitch, and then Tovey's switch of direction sprung an overlap and prop Price made it over in the corner.
Tovey's missed conversion was followed by a penalty miss from Paterson who was back on target in the 22nd minute, punishing the Dragons from 30 metres out.
But the men of Gwent turned the screw with a hat-trick of tries in the space of 11 minutes. Tovey, who missed a penalty just previously, cross for his try after following up on Ashley Smith's kick through. Tovey added the extras for a 10-10 scoreline.
Next over was flanker Lewis Evans who profited from a well-organised lineout drive which saw the Dragons forwards assert their dominance in that area.
Tovey converted and the industrious Smith closed out the first half's scoring with the bonus point score, which saw full-back Will Harries race up into the attacking line and provide the assist.
Into the second half, Tovey popped over a penalty from in front of the posts as the Dragons forwards maintained possession and continued to quell Edinburgh's attacking threats.
Coombs registered try number five when Edinburgh struggled to contain an advancing Dragons maul and the flanker peeled off the back to get the score.
Houston barged his way up close to the home line and Edinburgh worked some pick and go drives before Greig Laidlaw passed for Visser, who came in on a great angle to finish off a five-pointer.
The pace and quality of rugby dropped in the final quarter as both coaches took the opportunity to test out their reserves, mindful of the busy period of fixtures over the coming weeks.
The scores dried up, but Edinburgh managed to have the final say. Laidlaw took a quick tap and sent prop Cross crashing over for his second try of the league campaign.
Now up to eighth in the table, the Dragons are a point behind Edinburgh and have two games in hand on their Scottish rivals.
|Newport Gwent Dragons Score Card|
|Edinburgh Rugby Score Card|