Tom Court, Nick Williams, Ruan Pienaar and Darren Cave went over to secure the bonus point before the hour mark, with Andrew Trimble and Jared Payne adding further scores.
In response the Dragons went over through Andy Tuilagi but once Ulster got away the home side had no answer.
The Dragons made a quick start with consecutive bursts from Toby Faletau, who would later be forced off with a knock, and Tuilagi forcing Ulster to infringe at the breakdown.
Playing at full-back Tom Prydie made no mistake with the penalty, bisecting the uprights from just inside the Ulster half.
The home side added to that lead on eight minutes with another Prydie penalty after a great break from Will Harries, with Chris Henry penalised for slowing the ball down.
Ulster needed 15 minutes to get onto the scoreboard but when they did it was prop Tom Court who was the unlikely scorer.
Pienaar, playing at ten, tried to finish off what had been a period of concerted pressure and when he was stopped Court pounced on his offload to dive under the posts.
After Pienaar converted to make it 7-6, Prydie had the chance to put the home side back in front only for his third penalty attempt to drift wide but his South African counterpart did the same shortly after.
The Dragons had been impressive and on the half-hour they got their first try of the match through Tuilagi.
A barrage of pick and drives and clever switching of the play from scrum-half Jonathan Evans gave the Samoan centre a bit of space and despite a scrambling Ulster defence he battled his way over. Prydie converted to make it 13-7.
But almost as soon as the Dragons had retaken the lead, they found themselves under pressure again and could not stop Williams. The giant No.8 showed his strength on a rumble off the back of a ruck and when the Dragons failed to stop him at the first attempt he had too much power and scored the visitors' second try.
In a topsy-turvy first half the Dragons were back in front when Prydie slotted a third penalty but the full-back turned from hero to villain when he conceded a chargedown try.
Pienaar's grubber through was collected by Prydie but as he tried to clear the South African fly-half blocked his kick and dived over for Ulster's third try - his missed conversion leaving it at 19-16 at the break.
Ulster extended their lead to six with an early penalty in the second half from Pienaar and he added another a few minutes later to give the visitors a little breathing space.
The Dragons were then dealt a major blow when No.8 Faletau was forced off with an ankle problem to be replaced by Nic Cudd.
As the second half wore on a fourth Ulster try seemed inevitable and in the end it was centre Cave who drifted past Adam Hughes to score, Pienaar's conversion making it 32-19.
The Dragons had to score next but as they tried to force it Andrew Trimble showed great hands to intercept a Lewis Robling pass and the Ireland winger went under the posts as Ulster began to cut loose.
In the end Ulster had to wait until the 78th minute for their sixth score, replacement Payne getting on the end of an inside pass to go under the posts.
|Newport Gwent Dragons Score Card|
|Ulster Rugby Score Card|