Ospreys skipper Barry Williams praised the "guts" of his side after a thrilling Heineken Cup victory at Liberty Stadium.
The Ospreys went into the match against the French heavyweights on the back of several poor performances, but a superb defensive effort came to the fore as they clung to a five-point lead for the last quarter.
"Our defence was awesome," Williams said. "I couldn't ask for any more from the boys. It's turned our season around.
"We've been letting ourselves down lately, and we were due a big win. But we've set a standard and we have to keep to that standard."
The Ospreys went into the match without British Lions star Ryan Jones, Springbok winger Stefan Terblanche and former All Black fullback Adrian Cashmore, while Stade were missing the penetration of veteran winger Christophe Dominici and the experience of Pumas scrum-half Agustin Pichot.
The Ospreys were being helped by Stade fullback Juan Martin Hernandez, who missed simple two shots at goal, but both sides were rocked when home backrower Andy Lloyd and Stade centre Stephane Glas collided in midfield. Glas was helped from the pitch immediately, but the game was held up for seven minutes as Lloyd was treated and stretchered off.
Hernandez finally gave the scoreboard attendants something to do with a 35th-minute penalty goal, but visiting fans were silenced when fly-half Shaun Connor carved his way through the Stade defence and flicked it to centre Sonny Parker for the try. Connor added the extras and Parker produced a cracking tackle on winger Julien Arias to give Connor an easy shot at goal.
Hernandez made it three misses from four attempts in the opening exchange of the second half, and Arias dropped the ball over the line. To make matters worse for Arias, he was injured in the attempt and played no further part in the game.
Connor missed penalty and dropped-goal attempts and Stade burst back into contention when Argentinian winger Lucas Borges scored down the short side of a lineout. Hernandez, hardly surprisingly, missed the conversion.
Replacement Ospreys goal-kicker Matthew Jones made it 13-8 with his first shot at goal, and the home side bravely held out wave after wave of Stade attacks.
