Dragons wing Will Harries grabbed a hat-trick in a punishing second-half display.
The Welshmen scored seven tries as Edinburgh - forced to travel south by coach due to air travel restrictions - failed to build on a promising start.
The lead changed hands four times in a topsy-turvy first half which ended with Edinburgh trailing 20-14.
Home scrum-half Wayne Evans' burst into the cornerfor the first try of the game but, almost straight from the re-start, Edinburgh's Scotland international outside-half Phil Godman picked up on a loose ball and fed flanker Alan MacDonald to go over under the posts.
Godman's conversion put Edinburgh 7-5 ahead but a blast through the middle from 25 metres out by centre Ashley Smith restored the Dragons' lead.
Evans converted as regular kicker Jason Tovey was being treated for an injury which would end his match.
MacDonald was superbly tackled in the corner and Godman nearly scored from the ruck but was brilliantly wrapped up as he went over the line by flanker Gavin Thomas.
It did not help the Dragons cause either that loose-head prop Hugh Gustafson was sin-binned for dropping the scrum on his own line which, moments later, led to referee James Jones awarding a penalty try that gave Edinburgh a 14-12 lead.
Tovey's replacement, James Arlidge, restored the home advantage with a penalty and Harries increased it with a good try right on half-time.
Edinburgh endured a dismal second 40 minutes, missing tackles and creating little in the way of attack. Arlidge added another penalty after the break and Harries the other two tries before the hour to complete his hat-trick.
Edinburgh were now 21 points behind and could hardly expect to overcome their opponents.
But, with some renewed vigour in the final quarter, they gave themselves a slender hope as centre Ben Cairns went under the posts, with Godman's conversion meaning they could draw with two more converted tries.
However, any revival was killed off completely when wing Richard Fussell grabbed a sixth touchdown and full-back Martyn Thomas scored a spectacular 60-metre effort.
Edinburgh fought to get something out of the match and managed it when hooker Ross Ford came out of a pile of bodies with the ball and they secured their try bonus point.