Stade Francais (9) 37
Tries: Saubade, Parisse 2, Beauxis Cons: Beauxis 4 Pens: Beauxis 3
Scarlets (8) 15
Tries: M Jones, C Thomas Con: C Thomas Pen: S Jones
Mark Jones scored the opening try of the contest in France
Stade Francais overpowered the Scarlets with a superb second-half performance.
Mark Jones' try gave the Welsh side hope as they trailed 9-8 at half-time but they were blown away after the break as the French picked up the pace.
Julien Saubade opened the scoring for Stade, quickly followed by a double from his captain Sergio Parisse.
Ceiron Thomas scored a consolation in the closing minutes before Lionel Beauxis, who also put over seven kicks, scored a runaway final fourth try.
The Scarlets responded well to Beauxis' opening fifth-minute penalty as they attempted to break their eight-game Heineken Cup losing streak.
Their attacking play brought them level on 15 minutes with Stephen Jones slotting over a 30-yard penalty after the French side killed the ball on the floor.
Four minutes later a length-of-the-field break by full-back Morgan Stoddart put winger Jones in to outpace Beauxis from outside the 22 to put his side 8-6 up.
But Beauxis ensured the lead did not last, slotting over a fine 40-yard penalty to make it 9-8 to the home side at the interval.
Stade stepped up the tempo after the interval as Saubade crossed for his side's first try.
A quick display of hands by Juan Martin Hernandez and Beauxis put the winger over after 45 minutes to extend his side's lead to 14-8.
Beauxis continued his fine kicking display with a tight conversion from the touchline.
Parisse then scored his first try of the match on 49 minutes, breaking from the tail of a line-out.
The Italian passed the ball out to Scotland's Simon Taylor, and timed his run to finish off the move from two metres out after receiving a pass from Brian Liebenberg.
Beauxis interrupted his captain's flow with the conversion before Parisse crossed for his second score after 52 minutes.
This time the man-of-the-match used a more direct approach to plough over from a metre out as his fellow forwards turned up the pressure on the Scarlets defence.
The game turned into almost one-way traffic but the visitors managed to sneak a try of their own against the run of play with five minutes left.
Rob Higgett made a neat break down the right wing, drawing a defender to put in fellow replacement Ceiron Thomas unopposed under the posts.
But Stade would not be denied their bonus point as Beauxis charged down Thomas' attempted chip, collected the loose ball and ran in from 60 metres out.
The hosts remain unbeaten in all competitions this season and have now only lost once at home in 32 tournament matches.
The Scarlets, by contrast, have now lost their last nine games in Europe and following last weekend's loss to Harlequins, are facing an uphill battle to qualify for the knock-out stages of this year's competition.
Stade Francais: Beauxis; Arias, Glas, Liebenberg, Saubade; Hernandez, Oelschig; Roncero, Szarzewski, Attoub, Marchois, Taylor, Mauro Bergamasco, Rabadan, Parisse (capt).
Replacements: Blin for Szarzewski (66), Marconnet for Attoub (55), Tchale Watchoufor Glas (74), Bastareaud for Liebenberg (63), Camara for Roncero (71). Not Used: Vigouroux, Bouhraoua.
Scarlets: Stoddart; M Jones, King, G Evans, Daniel; S Jones, M Roberts; I Thomas, M Rees, Meeuws, Day, D Jones, S Easterby (capt), G Thomas, Lyons.
Replacements: Higgitt for Daniel (19), K Owens for M Rees (68), J Edwards for I Thomas (52), Martens for Roberts (52), C Thomas for S. Jones (66), J Turnbull for D. Jones (66), P John for Meeuws (66).
Referee: Peter Allan (Scotland)