Neil Doak's side were looking to make it five league wins on the bounce to climb to second in the table as they eye a spot in the Belfast final.
But it was the 10th-placed Dragons, who seven days earlier had been stunned by bottom club Zebre, who took the spoils thanks to tries by hooker Rhys Buckley, scrum-half Jonathan Evans and full-back Carl Meyer.
Ulster had to settle for the consolation of a losing bonus thanks to a late score by Ross Adair, adding to Craig Gilroy's brace.
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Ulster were on the front foot from the off, dominating possession and territory, yet it was the hosts that struck first with a penalty by wing Tom Prydie after 13 minutes.
The visitors responded on the quarter when Ireland international full-back Craig Gilroy finished off down the left after wing Rory Scholes sped through a midfield gap.
South Africa scrum-half Ruan Pienaar uncharacteristically shanked his conversion and the Dragons swiftly went back in front through another Prydie three-pointer.
Ulster were looking more dangerous with ball in hand but were faced with a determined Dragons defence and it was 6-5 at half-time, although Prydie was wide to the right of the posts with two long-range efforts in the closing stages.
The visitors were once again out of the blocks sharply from the restart and Pienaar, after a second woeful attempt from the tee, made it 8-6 with his third effort.
However, the Dragons came roaring back with fly-half Dorian Jones banging over a long-range penalty as Buckley - with Ulster prop Callum Black in the sin bin - crossing over from a driving lineout.
Ulster needed a charge in the final quarter to take the spoils, yet it was the unfancied hosts that stretched their lead to 21-8 in the 62nd minute when Evans dashed over from a ruck for a try that Jones converted.
Back came the Irish province with a second score by Gilroy after a break from captain Darren Cave but the Dragons secured their upset when full-back Carl Meyer finished strongly down the left after breaks by wings Ashton Hewitt and Hallam Amos.
At 26-15 up the hosts were in command but Adair dashed over from a quick lineout after 79 minutes to give Ulster a chance - but it was too little, too late.
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