The Scarlets secured a European Champions Cup semi-final place after Wales star Leigh Halfpenny masterminded victory over La Rochelle.
Halfpenny's 19-point haul, which featured five penalties and conversions of second-half tries from fly-half Rhys Patchell and centre Scott Williams, saw the Scarlets home 29-17.
The triumph at a sold-out Parc-y-Scarlets means they will face Leinster or Saracens next month for a place in the final.
It is the first time since 2007 that the Scarlets have reached the penultimate knockout stage of European club rugby's blue riband tournament.
And La Rochelle could have few complaints, despite tries by Romain Sazy and Piarre Boudehent, with scrum-half Alexi Bales kicking a penalty and conversion, and Benjamin Noble converting Boudehent's late touchdown.
The French side, making their Champions Cup debut this season, ultimately paid for that lack of experience, conceding several penalties through technical indiscipline, with Halfpenny landing seven from eight shots at goal.
The Scarlets, last season's PRO12 champions, will now await the outcome of Sunday's Leinster versus Saracens clash in Dublin, with a last-four encounter awaiting them at either the Aviva Stadium or Coventry's Ricoh Arena.
The Scarlets fielded 11 Wales internationals in their starting line-up under the captaincy of Scotland skipper John Barclay, but La Rochelle were without injured back-row forward Victor Vito and France international centre Geoffrey Doumayrou.
FINAL SCORE // SGÔR TERFYNOL pic.twitter.com/dfjaRUfXUp— Scarlets Rugby (@scarlets_rugby) March 30, 2018
La Rochelle were immediately under pressure as the Scarlets looked to keep ball in hand, and they fell behind after five minutes when Halfpenny kicked a penalty following a high tackle by Sazy on Ken Owens.
But the visitors responded impressively, sending juggernaut prop Uini Atonio through on a powerful charge before possession was kicked wide and sparked a touchdown scramble behind Scarlets' line.
And after lengthy deliberations between referee Luke Pearce and television match official David Grashoff, a try was awarded to Sazy, with Bales adding a touchline conversion in testing gusting conditions.
It was a definite alarm call for the Scarlets, but Halfpenny restored their advantage by kicking two further penalties after wing Paul Asquith departed injured. Asquith was replaced by flanker Josh Macleod, with Wales international openside James Davies moving to the wing.
Davies, an outstanding sevens player who helped Great Britain win an Olympic silver medal at Rio 2016, looked unfazed by his positional switch, and the Scarlets extended their advantage through another Halfpenny penalty nine minutes before half-time.
La Rochelle, though, finished the half strongly, and Bales made it 12-10 at the interval through an angled penalty, setting up an intriguing second 40 minutes.
Scarlets' Wales wing Steff Evans was forced off just five minutes after the restart when he was accidentally elbowed in the head while trying to make a tackle - Dan Jones replaced him - and another Halfpenny penalty hoisted his team five points clear.
La Rochelle's heavyweight pack, led impressively by replacement flanker Kevin Gourdon, began to sense dominance, keeping Scarlets pinned inside their own 22.
But the home side gained a crucial turnover just a metre from their own line, and cleared the danger just when it looked as though La Rochelle might breach their defence for a second time.
Not only did the Scarlets survive though, they stormed upfield and prised open La Rochelle's defence through centre Hadleigh Parkes' initial break, before Jones' long pass sent an unmarked Patchell surging over, with Halfpenny's conversion leaving the French team facing a mountain to climb.
The Scarlets saw replacement forward Will Boyde sin-binned 11 minutes from time, but it made no difference to the overall picture as Williams confirmed a semi-final spot by touching down five minutes from the end.