Wasps remained on course for a Heineken Cup Pool Six showdown with reigning European champions Toulouse next month after extinguishing the Dragons' fire with a 23-16 win at Cardiff City Stadium.
Wasps prevailed through tries by backs Ben Jacobs, David Lemi and Tom Varndell despite producing a performance that fell way below their best.
The Dragons, who led 10-0 and then 16-10, managed an early Ashley Smith touchdown and 11 points from fly-half Jason Tovey - a drop-goal, two penalties and conversion - before slipping to their third successive group defeat.
Dragons who came out firing, roaring 10 points clear in as many minutes. Tovey booted a 40-metre penalty to set the ball rolling, and with Wasps struggling to break free from their own 22, Wales wing Aled Brew sent Smith over unopposed with Tovey adding the extras.
Dave Walder opened the visitors' account with a penalty after his first attempt hit the post, but the Dragons continued to press as they maintained territorial dominance.
Wasps, though, drew level in enterprising fashion, England lock Simon Shaw turning defence into attack through some superb work inside his own 22 before Jacobs and Lemi combined to take play a further 60 metres downfield.
And with the Dragons on the back foot defensively, Jacobs sliced through a gap to score. Walder converted to make it 10-10, and then kicked another penalty, but only after a Tovey penalty and drop-goal restored the home side's advantage.
But Wasps had a reliable points source in Walder, who added another penalty just before the break, enabling the Londoners to troop off 16-13 adrift.
Centre Steve Kefu ghosted through the Dragons defence, and Lemi did not require any second invitation from 20 metres out, scoring with his trademark celebratory dive. Although Walder missed the conversion, Wasps led for the first time as Tovey was helped off to be replaced by Matthew Jones, who immediately missed a long-range penalty chance.
A combination of excellent ball-retention and repeated excursions across the gain-line took its toll on the Dragons defence, and Varndell was the beneficiary as he claimed Wasps' third try.