The Dragons looked to have it all wrapped up at 16-10 with only six minutes remaining, but the visitors had other ideas as they produced some scintillating rugby to maintain their 100 per cent start to the season.
The Dragons took full advantage of some poor Ulster discipline as Craig Warlow landed two penalties and a drop goal to give Newport a 9-0 lead at the break.
It seemed to be all over when Warlow converted Ian Gough’s try six minutes into the second half, but apart from one more penalty from Warlow, the Dragons ran out of puff.
A superb try from centre Andrew Trimble in the 48th minute started the fight back for Ulster and with Paddy Wallace’s boot finding it’s target, Ulster were soon back in the game.
Wallace converted a Neil Best touchdown and put over a penalty to deny the Dragons despite some sterling work from skipper Jason Forster.