Dragons claimed their first win in Pool 1 with a 28-21 success at bottom side Enisei-STM.
Captain Cory Hill, Jared Rosser, Hallam Amos and Charlie Davies all scored tries for the visitors, who wrapped up a try bonus point.
However, Dragons were made to hold on for the victory when Anton Rudoy's late try was converted by Yury Kushnarev.
Siya Masuku kicked 21 points and controlled the game masterfully from flyhalf as South Africa's Sharks defeated Gloucester 36-22 in the final of the European Challenge Cup at the Tottenham Hotspur Stadium on Friday.
Juan Pablo Socino will miss Newcastle Falcons' opening European Challenge Cup fixtures after being handed a two-week suspension by the RFU's disciplinary panel.
Holders Saracens and triple European title winners Toulon will meet in the pool stage of next season's Champions Cup.
England duo Joe Marler and Owen Farrell have both received citings following the weekend's European semifinals.
