Tries from captain Chris Pennell and Marcel Garvey, converted by Joe Carlisle, saw Worcester into a commanding lead in the opening 12 minutes.
But 18 points from the boot of Felipe Contepomi and a try from Paul Sackey put the game beyond the Warriors.
It was hugely disappointing for the home fans, who saw their side race out of the blocks but fail to score a single point after the 12th minute, thus failing even to claim a losing bonus point.
Pennell was first to go over after six minutes, with Carlisle converting, as he did six minutes later when Garvey crossed for the second.
At that point the Warriors were well on top and in line for a creditable victory over their illustrious opposition.
But Contepomi booted over two penalties, the first after half an hour and the second on the stroke of half-time, to give his side a foothold.
And it was the boot of the Argentinian that continued to do the damage after the restart as further penalties in the 45th and 50th minutes put them within two points of their opponents, before his fifth of the night in the 57th minute put them in the lead.
Stade were on top, now, and they confirmed their dominance five minutes later when Sackey showed strength and composure to go over in the corner for the French side's first try following good work from Contepomi.
Contepomi could not convert, but the fight had gone out of the hosts and he added insult to injury with his sixth penalty five minutes from the end.
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