Tom Prydie booted the Dragons into an early lead and they trailed by just three points at the interval following a try from Andy Tuilagi.
But the floodgates opened following the break and Ulster added to first half scores from Tom Court, Nick Williams and Ruan Pienaar through Darren Cave, Andrew Trimble and Jared Payne.
Tom Prydie quickly booted the Dragons into the lead at Rodney Parade and he doubled his side’s advantage on eight minutes.
But Ulster, who have not lost a competitive match this season, were threatening and they got their breakthrough on the quarter-hour mark.
Pienaar made the initial inroads with a half-break, he flicked the ball inside and Ireland prop Tom Court picked the ball off his toes to score.
The South African converted to give his side the lead but it was short-lived as the Dragons rallied.
Darren Edwards’ side went through 15 phases before Tuilagi crashed through Ulster’s defence to score.
But Ulster continued to exert pressure and they went back in front following some soft defending from the hosts and Nick Williams crashed through two defenders to score.
Prydie hit-back as the topsy-turvy nature of the encounter continued but Ulster made a crucial breakthrough minutes before the interval.
Pienaar slotted a kick through and then charged down Prydie’s clearance to hand his side a 19-16 half-time lead.
Pienaar and Prydie exchanged shots at goal early in the second-half but Ulster quickly exerted their dominance and they put the Dragons to the sword in emphatic fashion.
Cave wrapped up the bonus-point just before the hour mark but that was not enough for Ulster who capitalised on Dragons’ mistakes through Trimble and Payne
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