Second-half tries from Rhys Patchell and Scott Williams earned Scarlets a 29-17 win over La Rochelle and a place in the Champions Cup semifinals.
The hosts were made to soak up a considerable amount of pressure in a match that never really caught fire as expected, before Patchell and Williams crossed the whitewash in the final quarter.
Leigh Halfpenny had kept the scoreboard ticking for the hosts before that and ended the match with 19 points.
La Rochelle claimed the game's opening try through Romain Sazy while Pierre Boudehent raced the length of the pitch to add a late consolation, but they were foiled by their own indiscipline.
Scarlets' reward for their win is a Champions Cup last-four clash with either Leinster or Saracens, who meet in Dublin on Sunday.
The first half failed to live up to the pre-match hype as the two usually expansive sides played out a cagey opening 40 minutes.
Scarlets got the scoreboard ticking through the boot of Halfpenny but it was the visitors who breached the tryline first, to silence the capacity home crowd.
Following a moment of magic from Arthur Retiere, who chipped over the Scarlets defence before gathering inside the 22, fly-half Jeremy Sinzelle put the ball in the air with a penalty looming.
As the ball bounced around the in-goal area on the visitors' right wing, Sazy thought he had touched down. The celebrations were muted but after referee Luke Pearce went upstairs, TMO David Grashoff decided the La Rochelle captain had won the race to the ball a fraction ahead of Halfpenny.
The hosts were not entirely convinced by Grashoff's decision, but La Rochelle would be hamstrung by a large penalty count as Halfpenny converted three unanswered attempts to give his side a five-point lead late in the half.
That was reduced to two on the stroke of half-time, however, as Bales -- who endured an indifferent afternoon kicking out of hand -- slotted a penalty through the uprights.
Halfpenny extended the Scarlets lead with another penalty shortly after half time, but it was the visitors who began the second period on the front foot.
And with around 25 minutes to go the hosts were forced to withstand wave after wave of La Rochelle pressure as they dug deep in the face of a series of penalties close to their own line.
Tadhg Beirne was probably fortunate not to see yellow -- as he was later in the half -- when he collapsed one drive as it neared the tryline.
However, referee Pearce opted to keep his card in his pocket and within seven minutes the hosts had scored a try of their own.
Hadleigh Parkes did excellently to pirouette out of a tackle and into the La Rochelle 22, and as the ball was recycled Patchell backed himself to beat his man and cross the line.
Halfpenny made no mistake with a difficult conversion, and the Scarlets lead was an intimidating 12 points with less than a quarter of the match to play.
Beirne again avoided a sin-binning as La Rochelle were denied again following a smart break from Tawera Kerr-Barlow and Steeve Barry. With time running out Will Boyde was shown a yellow card.
The 14 men did not buckle, though, and after some excellent handling by James Davies on the right wing Scott Williams crossed for the try that secured their place in the last four.
Pivac's Scarlets ended the match on the attack, but just as it looked as though they would cap victory with a third try Kevin Gourdon stripped the ball before Boudehent sprinted in from 85 metres.
It was too little, far too late and did little to dampen emotions in west Wales as the Parc y Scarlets erupted at full time.
