Two second-half tries from Nic Fitisemanu and Nathan Brew were the cornerstones of the Dragons’ fightback at Rodney Parade.
Edinburgh had led 10-0 at half-time, as a combination of dreadful conditions and autumn international absences kept scoring to a minimum.
Gunners’ winger David McCall opened the scoring after 11 minutes with a try converted by Duncan Hodge. It had come against the run of play, following Colin Charvis and Aled Brew spills with the line at their mercy.
These were compounded by Mike Hercus’s penalty miss 13 minutes before the break and Hodge’s three-point success in first-half injury-time.
The Dragons made wholesale changes after half-time, and after replacement Nic Fitisemanu’s try – converted by Craig Warlow – they took control.
Nathan Brew’s 70th-minute try gave the Welshmen the lead for the first time which, with Aled Thomas’s conversion and late penalty, they did not relinquish.