Stade Francais: (9) 19
Arias finished off a fine sweeping Stade move in the 70th minute
Tries: Corleto, Arias
Pens: Skrela 3
Bristol: (3) 11
Pens: Strange 2
Second-half tries from Ignacio Corleto and Julien Arias helped Stade Francais to victory against Bristol in the Heineken Cup Pool 3 match in Paris.
Stade led 9-3 at the break thanks to three penalties from David Skrela.
Two penalties from Jason Strange closed the gap before Corleto extended the lead with a fine 54th-minute try.
Bristol responded through a Tom Arscott try, but a sweeping move from Stade was neatly finished by winger Arias in the 70th minute to secure the victory.
The defeat means Bristol slip to third in the group and must beat leaders Cardiff next Sunday to maintain any hopes of qualifying for the quarter-finals.
Referee George Clancy was quickly in to the action on 12 minutes when he sent props Rodrigo Roncero and Jason Hobson to the sin-bin for fighting.
Skrela's boot had given Stade a six-point lead at the break, but the home side should have been further in front had Remy Martin scored in the 24th minute.
The flanker had two support runners alongside but opted to go for glory himself, only to be denied by a fine try-saving tackle from Luke Arscott just inches from the Bristol line.
Although Strange's second penalty closed the gap to three points at the start of the second half, Stade extended their lead when Argentine Corleto held off two defenders to touch down in the corner.
Bristol hit back five minutes later after fine work from Brian O'Riordan helped Tom Arscott to five valuable points which Strange failed to convert.
But Arias wrapped up the win 10 minutes from time thanks to excellent link-up play from Skrela and winger Christophe Dominici.
Bristol coach Richard Hill:
"We gave Stade Francais a scare. It looked like we might have a real chance of winning the game but in the end, I don't think we controlled it like we should have done in the second half.
"We didn't use the elements as we should have and we made a few unforced errors.
"But we weren't disgraced. The players had a real optimism that we were going to win the game tonight and that is good. We just needed that extra five or 10% in the second half.
"It's a tough one but we aren't out of it. We'll give it one last go. If we get it right next weekend and get five points, it could be enough."
Stade Francais: Corleto, Arias, Glas, Bastareaud, Dominici, Skrela, Albouy, Attoub, Szarzewski, Roncero, Marchois, Pape, Rabadan, Martin, Parisse.
Replacements: Weber, Montanella, du Plooy, M. Bergamasco, Fillol, Beauxis, M. Bergamasco.
Bristol: L. Arscott, T. Arscott, Higgitt, Brew, Lemi, Strange, O'Riordan, Crompton, Regan, Hobson, Winters, Hohneck, Salter, El Abd, Blowers.
Replacements: Linklater, Clarke, Attwood, To'oala, Pennycock, Beveridge, Hill.
Referee: George Clancy (IRFU)