The Dragons recored am impressive 32-15 victory over Bayonne in France, while Pool rivals Bristol struggled to a 33-19 win at home agaist Bucuresti.
In the other match of the evening Glasgow and Saracens drew 6-6, meaning both sides qualify for the final eight.
A Kevin Morgan double powered the Dragons into the European Challenge Cup quarter-finals.
Playing the bottom side in the European Challenge Cup's Pool 1, Paul Turner's side turned an 8-3 halftime deficit into a bonus-point victory to finish ahead of Pool 1 rivals Bristol.
With both sides finishing on 25 points, it came down to tries between them in the Pool stages, and the Dragons edged it 2-1. But it took a second-half double from skipper Morgan to secure the crucial points.
Dragons fly-half Ceri Sweeney opened the scoring with a penalty goal in only the third minute, before locks Cedric Bergez and Luke Charteris were sent to the sin-bin for exchanging blows in the ninth minute. The home side made the most of the 14-a-side game when No 8 Marc Baget rumbled over for the game's opening try.
The Dragons' hopes of European silverware were looking slim when Bayonne fly-half Henri-Pierre Vermis slotted a penalty goal on the half-hour mark, and the home side - who were below even Bucuresti in the Pool before the match -book an 8-3 lead into halftime.
Winger Aled Brew brought the Dragons back into the match with a try in the corner in the 44th minute, but they were left to rue poor defence when Vermis threw an outrageous dummy in the 55th minute. No one in the crowd fell for it, but the Dragons players all seemed to as the Bayonne fly-half ghosted in for a try under the posts. His conversion simply twisted the knife and American international Paul Emerick's yellow card didn't really help matters.
Despite their one-man disadvantage, Wales back-rower Michael Owen inspired the comeback with a huge skip-out pass to put in-form skipper Morgan over. Sweeney added the extras to level the scores, and the Dragons took the lead when replacement backrower Andrew Hall scored.
The home fans at Stade Jean Dauger were stunned into silence in the 74th minute when Morgan completed a superb sequence of phases from the halfway line, and Sweeney added the conversion to give his side an unassailable lead as Bayonne gave up hope of an upset.
Sweeney added a late penalty to send the home fans home happy.