Victory for the capital club sees them move to within a point of leaders Clermont, who play Biarritz at home on Sunday.
Geoffrey Doumayrou crossed the line on 25 minutes to open the scoring for Stade but the hosts could not build on that early advantage and went in at the break leading just 8-3.
A second try did arrive in the 69th minute though, South African fly-half Meyer Bosman touching down before Morne Steyn converted to open up what proved to be an unassailable lead.
Steyn then added three penalties as Stade rounded off their victory.
"Mission accomplished," said Stade coach Gonzalo Quesada. "We missed a few chances at the end. We knew Grenoble would be tough to beat, so we're satisfied to have had control of the ball but we're a little disappointed not to have taken the bonus point."