Matt Scott, the Scotland centre, was the main player to rise above the mediocrity as he helped to create the first try and then scored the second to make up for the forward pressure the visitors were facing all evening.
However, the rest of the drama came in the final two minutes as the Dragons chased the victory they required to keep alive their own faint hopes of a top-six finish in the RaboDirect PRO12.
They earned scrum penalty after scrum penalty on the Edinburgh line, but the visitors were able to hold strong and finally turn the Dragons eight to claim an unlikely victory, with celebrations to match.
There had been further warnings from the Irish referee Leo Colgan but, having harshly sent one Edinburgh player to the sinbin, he seemed reluctant to send a more deserving candidate thereafter. It brought a first away victory in the league this season for Edinburgh and kept alive hopes of a place in the new-look European top flight next season.
This match was played on an unusual evening and with an unusual kick-off time because it is a European rugby weekend, and the rules say that a domestic game cannot clash.
The original match having been postponed because of a waterlogged pitch in January, the conditions were familiar, with the rain pouring down. Never mind the sub-Saharan smog that was meant to be smothering South Wales, these were good old-fashioned rain clouds which descended over Rodney Parade, making conditions tough for both teams.
The Wales wing Hallam Amos was playing his first game back from injury and breezed through the middle of the Edinburgh defence only to lose the ball as he went for the corner. Even more worrying for the visitors were the early scrums, with the Dragons, who have struggled up front against almost everyone and conceded four setpiece tries to Connacht, getting on top of the Edinburgh eight.
The visitors were relieved that the early home pressure led to only a Jason Tovey penalty, though he doubled that lead before half-time with another penalty from a collapsed scrum. Edinburgh landed a penalty themselves through the full-back Jack Cuthbert and then, having threatened nothing for the first 37 minutes, suddenly took the lead with a pretty good try.
Scott made the half break, drew the defence and put fellow centre Andries Strauss into space. He made it up to the line and then the tighthead prop Willem Nel barged his way over the final few feet for the try, converted by Cuthbert.
Dragons earned a penalty from the kick off so they went in at half-time just one point behind but no doubt scratching their heads as to why they were not well ahead, having dominated territory and possession.
They did get back into the lead just after half-time with another scrum penalty kicked by Tovey, but it was shortlived as Scott again dragged his team back into the contest.
He burst powerfully into an attack which had been struggling to get over the gain line and not only achieved that but went 30 metres to score under the posts. The Scotland man was just about the only player on either side to rise above the gloom.
Cuthbert converted and the idea of a bonus-point win which would keep them in the European race was still alive. It also kept Cuthbert's impressive kicking record of landing every one following an early miss from almost 50 metres.
Another Cuthbert penalty and the win seemed safe, but it proved to be anything but. Dragons drove a lineout into the Edinburgh 22 and Izak van der Westhuizen was deemed to have pulled the drive down deliberately. It was a first warning but he was still given a yellow card and Edinburgh were down to 14 men for the last nine minutes of the match which gave the home side renewed belief.
From that period of pressure, the replacement centre Ross Wardle picked a good line close to a ruck on the line and he was able to crash over. Tovey converted to bring his side within four points and set up the furious finish. Dragons chose scrums rather than a kick to the corner and another driving lineout, partly because that had been such a strong area all evening for them. In the end it was to prove their undoing at the most vital time of all.