Northampton claimed a bonus-point win over Scarlets but must wait to see if they have reached the Champions Cup quarter-finals.
Saints needed maximum points from their final Pool Three game to stay in with a chance of progressing as one of the best three runners-up.
And they did it with ease, thanks to tries from Harry Mallinder, George Pisi, Sam Dickinson and George North.
Sunday’s results will determine whether Northampton make the last eight.
Saints will not progress if Pool Two challengers Ospreys and Clermont Auvergne both win their games – Clermont with a bonus point – and Pool Four hopefuls Stade Francais see off Leicester with maximum points.
Scarlets had nothing left to play for in the competition as they sit bottom of the pool, but the home crowd left happy on Saturday night after seeing their side grab a late consolation try through Rhodri Jones.
The Premiership visitors took an early lead when Mallinder, son of director of rugby Jim, intercepted a loose Scarlets pass and sprinted home.
Saints struck again eight minutes later as Pisi went over in the corner, before Aled Thomas slotted the hosts’ first points from the tee to make it 12-3 at the break.
Dickinson claimed a simple touchdown after the restart and Scarlets’ woes continued when lock Maselino Paulino was yellow-carded for a shoulder barge on England’s Courtney Lawes.
Wales international North secured the important bonus point when he crossed the line after a brilliant pass from Mallinder.
Saints finished with 14 men after replacement scrum-half Lee Dickson was sin-binned for a technical offence, and it gave Jones the chance to touch down at the death.
Scarlets head coach Wayne Pivac: “We wanted to be in the game, and over the 80 minutes we put in a solid performance.
“It was a big step up from last week.”
Northampton director of rugby Jim Mallinder: “It’s always a challenge, particularly to get the four tries, so we are delighted to get the bonus point.
“We knew that whatever team Scarlets put out they would be fighting. We can sit back and hope that results go our way on Sunday.
“Not getting any bonus point wins has made it difficult for us and made it close, but to win four and draw one is pretty good.”
Scarlets: Michael Collins; Tom Williams, Regan King, Steven Shingler, DTH van der Merwe; Aled Thomas, Gareth Davies; Phil John, Ken Owens (C), Samson Lee; Tom Price, Maselino Paulino; Aaron Shingler, Will Boyde, Morgan Allen.
Replacements: Kirby Myhill, Dylan Evans, Rhodri Jones, Lewis Rawlins, Tom Phillips, Aled Davies, Josh Lewis, Steff Hughes
Sin Bin: Paulino (48).
Northampton: Ben Foden; Jamie Elliott, George Pisi, Harry Mallinder, George North; Stephen Myler, Tom Kessell; Alex Waller, Dylan Hartley (c), Paul Hill; Courtney Lawes, Christian Day; Jamie Gibson, Tom Wood, Sam Dickinson.
Replacements: Mikey Haywood, Ethan Waller, Gareth Denman, Michael Paterson, Jonathan Fisher, Lee Dickson, JJ Hanrahan, Luther Burrell.
Sin Bin: Dickson (73).
Ref: Pascal Gauzere (France).
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