Replacement fly-half Ben Botica secured Harlequins a last ditch win against the Scarlets to qualify for the Amlin Challenge Cup quarter-finals.
Botica, whose father Frano played for the Scarlets, landed a 77th minute penalty at Parc Y Scarlets.
Harlequins will face Stade Francais in Paris in the last eight in a repeat of the Amlin Challenge Cup final of 2011.
The Scarlets defeat means there are no Welsh sides in the knockout stages of either European competition.
The disappointing performances of the Welsh regions in Europe comes against the background of the ongoing row with the Welsh Rugby Union over funding, the exodus of players and an Anglo Welsh league.
Harlequins, the Scarlets and the Cardiff Blues were all in the hunt for the last remaining Amlin Challenge Cup qualification place before kick-off, but the English side secured the final place with this win.
The home side had led for the last 30 minutes of the game thanks to tries by scrum-half Gareth Davies, flanker Aaron Shingler and centre Scott Williams.
Quins had matched them all the way in a titanic tussle played in torrential rain with three tries of their own by full-back Michael Brown, winger Ollie Lindsay-Hague and scum-half Karl Dickson.
But Botica stepped up, with regular kicker and fly-half Nick Evans limping with a leg injury, to land the crucial blow against a side his father - former All Black Frano - had played for in the nineties.
The home side had made the perfect start with a superb counter-attack try inspired by fly-half Rhys Priestland inside his own half.
The Welsh international set winger Jordan Williams free and delivered the scoring pass to allow scrum-half Davies to race in for a superb try. Priestland added the extras to make it 7-0.
But minutes later, the Scarlets were down to 14 men when flanker Shingler was yellow carded for an illegal tackle by French referee Jerome Garces.
Harlequins took full advantage and made their extra man count when England full-back Brown finished off a simple passing movement to run in unopposed for a try.
Fly-half Evans' conversion levelled the scores at 7-7 before winger Williams failed with a long-range penalty for the Scarlets.
Harlequins then took the lead with a move started and finished by winger Lindsay-Hague, making his first Heineken Cup start, who showed some impressive footwork and deft passing in the move for his try.
Evans converted before opposite number Priestland replied with a penalty and the home side took the lead when Shingler made amends for his earlier misdemeanour with the Scarlets' second try.
His quick-thinking saw him pounce on a loose ball at the back of ruck on the Quins line to make it 15-14 to the home side at half-time.
Harlequins hit back right after the break with England captain Chris Robshaw orchestrating an impressive forward drive to allow scrum-half Dixon to scamper in for a try down the blind-side to restore his side's lead.
The Scarlets then replied with another impressive counter-attack try which saw Wales centre Scott Williams finish off from short range for his second try against the Londoners and his fourth try in the Heineken Cup.
Priestland missed the conversion, but the Scarlets were 20-19 ahead.
Centre Williams then made a 50m break from behind his own try line but the move ended when his pass on halfway was ruled forward.
Winger Williams and Priestland then both failed with two penalty attempts for the Scarlets, before Botica stepped up to land the winning kick against his father's old side.
Quins boss Conor O'Shea: "It was harem-scarem out there. It is a delight to play against a team like the Scarlets, it really is.
"Both teams tried to play in a way that should be lauded - given the conditions, I thought it was an incredible game.
"To finish as one of the best runners-up in such a tough pool is a real credit to the guys. We are now going to play against Stade Francais away, and the juices will really flow for something like that."
Scarlets head coach Simon Easterby: "We competed against a really good Quins team and for large parts we were better than them, but in the second half they kept coming back at us and we eventually gave away a bit of a soft penalty for them to get ahead.
"We've competed against every team [in the pool] for large periods, but we had a chance today, and we blew it.
"This European Cup has thrown up a huge amount of good games. It is disappointing that we did not take our opportunity and get into the Amlin quarters."
Scarlets: A Thomas; K Phillips, Maule, S Williams, J Williams; Priestland, G Davies; John, E Phillips, Lee, Ball, Earle, A Shingler, Barclay, McCusker.
Replacements: Turnbull for John (58), Adriaanse for Lee (77), Snyman for Earle (55), Evans for Barclay (58).
Not Used: Myhill, R Williams, Warren, Owen.
Sin Bin: J Williams (10).
Harlequins: Brown; Lindsay-Hague, Hopper, Molenaar, Monye; Evans, Dickson; Marler, Ward, Collier, Kennedy, Robson, Guest, Robshaw, Easter.
Replacements: Williams for Lindsay-Hague (58), Botica for Monye (65), Stuart for Evans (77), Matthews for Kennedy (55), Fa'asavalu for Guest (70).
Not Used: Gray, Lambert, Doran-Jones.
Ref: Jerome Garces (France).