Four penalties and a drop goal from fly-half Jason Tovey and a momentous rearguard action in the closing moments were the key points to the Dragons' victory.
Number eight Roger Wilson got an Ulster try in the first half while outside-half Paddy Jackson landed the solitary penalty for the Irishmen.
It was a shock for the men from across the water. Ulster are looking to get off to the same flying start in September that they had last season when one of their victims were the Dragons, thrashed 46-19 at Rodney Parade.
This season, the Welshmen were first to face last season's league runners-up before Ulster tackle games at home to Glasgow and Benetton Treviso, plus a visit to Connacht before the end of the month.
And such are the resources at Ravenhill that even without stars like Ruan Pienaar and British Lions Rory Best and Tommy Bowe in the side, head coach Mark Anscombe could still name a glittering array of seven Irish internationals and one South African in the starting XV with another three Irish caps on the bench.
However, there have been a lot of changes at Dragons over the summer with the arrivals of head coach Lyn Jones, assistant Kingsley Jones, the appointment of new chief executive Gareth Davies and a couple of players bringing renewed optimism that the perennial league basement dwellers could finish much further up the table this time.
There was a minute's silence before the match for the wife of former Newport benefactor Tony Brown and Welsh icon Cliff Morgan.
And it was Tovey who got the match going inside 10 minutes after a long penalty miss saw him land an equally long drop goal.
Ulster's young Jackson then levelled the score with a penalty of his own. The Irishmen looked keen and had the Dragons' pack on the back foot at times.
After Tovey had added his second goal of the night, this time a penalty from 40 metres to put his side three points in front, the Ulster pack got on top. Jackson put a penalty into touch close to the home tryline and, from there, the visiting eight drove the home side backwards, leaving number eight Roger Wilson to claim the try at the base of the ruck.
That put Ulster 8-6 up and the remaining 15 minutes turned into a bit of a stalemate.
Jackson looked to land another couple of penalties, one from 38 metres and the other a straightforward 25m effort, but both went wide of the uprights while Tovey tried to add his third kick of the night but that too was wayward.
Ulster threatened in the second half with a couple of breakaways from their own half, one of which saw Jackson fired a cross-kick wing David McIlwaine only for it to trickle into touch.
The Dragons fought bravely but it only seemed a matter of time until Ulster got the try.
The moment of the match came at the end when the Irishmen camped themselves on the home line. Time and again, with just inches to the try, the visiting pack pounded the Dragons but the defiant defence held out for a win which sent the home crowd into raptures on the final whistle.