Scarlets (16) 31
Tries: Lyons, J Davies (2) Cons: S Jones (2) Pens: S Jones (4)
Stade Francais (5) 17
Tries: Bousses (2), Bergamasco Cons: Beauxis
David Lyons gets the opening try in a scorching start by the Scarlets
The Scarlets ended an 11-game win-less run in Europe, dumping Stade Francais out and sending Harlequins into the quarter-finals as pool four winners.
An early try from David Lyons and Stephen Jones' boot helped the home side to an early 13-0 lead in Llanelli.
Guillaume Bousses and Jon Davies each exchanged braces of tries, Jones' kicking extending the lead to 31-10.
The French visitors got a late try from Italian international Mirco Bergamasco, but it was mere consolation.
The last time Scarlets were successful in Europe, they beat Munster in the 2006-2007 quarter-finals.
Already out of quarter-final contention with just a draw to their name from their previous four outings, the Scarlets were in positive mood as centre Regan King sent Lyons in from 10 metres out.
Stade's direct approach was getting little change out of the Scarlets' defensive line, until Bousses barged over on 16 minutes after the intervention of the TV official.
A clash of heads between Lyons and Juan Hernandez saw both off to the blood bin, the latter failing to return.
The French team got themselves into a good attacking position in the opening exchanges of the second half but failed to make it count as they gave away a penalty in the Scarlets' 22.
The Scarlets lost a chance of a try at the other end when Regan King intercepted but prop Phil John was unable to squeeze in at the right corner.
Jones kept his side's scoreboard ticking with 16 points
But it mattered little to the Welsh as they scored a second try on 55 minutes, Davies running in from 25m out after an exquisite inside pass from King.
A wayward pass from replacement hooker Ken Owens saw Bousses intercept and run in unopposed from halfway.
However, the wing's drop-kick conversion attempt from right in front of the posts rebounded off the left upright.
A fine Scarlets performance was rounded off when Davies raced in from halfway for his side's third try.
Stade had the final say when wing Bergamasco went over in the right corner for his side's third try, Lionel Beauxis' conversion proving his side's only successful kick.
The result provides a boost for the Scarlets' Welsh rivals the Ospreys, knocking Stade out of contention for a best runners-up spot.
Scarlets coach Nigel Davies said:
"We knew that individually we would have to play at the top of our game and collectively we would have to do the same, and I think we showed what we are potentially capable of.
"We said that today was about putting in a performance for 80 minutes and I think we did that.
"I thought the guys had complete belief in themselves and the performance was outstanding. We have still got a lot to do.
"Jon Davies has got a huge amount of pace in his game and he is powerful. We saw what Jon is capable of moving forward.
"We have done Harlequins a favour, but it was more about us and re-establishing some European credentials."
Stade Francais coach Ewen McKenzie said:
"We weren't good enough. We weren't even in the same street.
"I'm very disappointed. I thought we were very soft at the start of the game. Once they got 13 points up it was going to be very hard.
"We didn't go out there to play stupid football early on, but we just never got out of the blocks in the physical stakes. The key players played well for them and we didn't do much at all.
"In a big game we have come up short and we will have to look at that to see the reasons why."
Scarlets: C. Thomas, Daniel, King, Davies, Williams, S. Jones, Roberts; John, Rees, Manu, Cooper, Day, Easterby, Edwards, Lyons.
Replacements: Martens for Davies (76), Cattle for Roberts (72), I. Thomas for John (48), Owen for Rees (55), Maling for Day (62), D. Jones for Edwards (26). Not Used: Turnbull.
Stade Francais: Beauxis, Mi. Bergamasco, Glas, Liebenberg, Bousses, Hernandez, Oelschig; Marconnet, Szarzewski, Attoub, Marchois, Taylor, Parisse, Ma. Bergamasco, Leguizamon.
Replacements: Gasnier for Glas (56), Bastareaud for Hernandez (40), Albouy for Oelschig (60), Sempere for Szarzewski (50), Montanella for Attoub (40), Rabadan for Marchois (50). Not Used: Vigouroux.
Referee: Dave Pearson (England)