Clermont, without key backs Wesley Fofana, Jonathan Davies and Noa Nakaitaci, have now lost 11 of their 12 French top flight finals and also lost to Toulon in the inaugural European Rugby Champions Cup final at Twickenham last month.
Scrum-half Morgan Parra missed a penalty after four minutes as Clermont dominated early on but Julien Bardy picked up a yellow card for a dangerous tackle on Nayacalevu Waisea and it got Stade Francais going.
Springbok fly-half Steyn converted the resulting penalty kick and slotted home two more to pad the lead to 9-0 after 30 minutes.
Camille Lopez reduced the deficit on the stroke of halftime to make sure Clermont stayed in contention. The France fly-half was replaced by Brock James in the 51st minute and the Australian cut the deficit to three points with a penalty as the Parisians were sanctioned for collapsing a maul.
But he missed a 23-metre penalty 10 minutes from time and instead it was Steyn who slotted home his fourth of the night to wrap it the title.