The French side weathered a strong Gloucester start to reach the interval at 10-10 and Stade centres Jonathan Danty and Geoffrey Doumayrou crossed the line to secure a deserved victory for their team.
England winger Jonny May gave Gloucester an early lead when he intercepted a pass before scorching to the line, but Italy number eight Sergio Parisse took advantage of a knockback close to the line to cross for Stade.
Another interception allowed Danty to run in a try midway through the second half and Doumayrou showed quick feet to scamper over for a brilliant individual score that gave Stade a cushion.
Flanker Ross Moriarty grabbed a late consolation try for Gloucester who won the Challenge Cup in 2006 and 2015.
"We have come through a very difficult season in Paris but this team have come through it. I'm very proud of the team," Parisse told Sky Sports.
"We tried to follow our philosophy. It wasn't easy because Gloucester put us under pressure.
"Maybe we didn't play our best game, but congratulations to the boys."
(Reporting by Ed Osmond; Editing by Ken Ferris)
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