Reigning champions Toulouse beat Munster on penalties after reacting to draw 24-24 in Dublin on Saturday and reach the European Cup semi-finals.
In the second shootout in the competition’s 27-year history alone, Conor Murray missed once and Ben Healy twice, while Toulouse scored their first four kicks.
In the previous shootout, the Leicester Tigers beat Cardiff in the 2009 round of 16.
“Against a great team, we will keep the memory of what we did here, it’s powerful,” Toulouse winger Thomas Ramos told France Televisions.
“It was a crazy match, with an unusual ending, we held our heads better than them. We found it difficult today, but we’re still there. “
The French club will return to Dublin to face Leinster next weekend after the Irish province beat the Tigers 23-14 at Welford Road later in the day.
Jamison Gibson-Park, aided by the Leinster scrum, was impressed by Toulouse.
“They are an incredible team, they went to Ireland today and won, which shows how good they can be,” Gibson-Park told BT Sport.
“We will take it one day at a time and prepare as best we can for next week.”
There were over 40,000 at Aviva Stadium, for a match moved to the Irish capital due to two Ed Sheeran concerts at Munster’s Thomond Park in Limerick.
In the 19th quarter-final for both sides, Alex Kendellen gave Munster the lead at the start, but Romain Ntamack, France’s opening half, responded after 12 minutes.
Just before the half hour, the winger of the Bleus Matthis Lebel passed for a corner following a dominant scrum of the guests.
Irish opener Joey Carbery missed a penalty in the 34th minute before atoning by preparing Keith Earls and converting the try to bring the score to 14-14 at half time.
Munster controls the game after half-time.
Carbery missed a penalty but winger Mike Haley crossed after just four minutes of the second half.
Toulouse manager Ugo Mola then sent three of the national team forwards to the bench waiting for his bench, including Grand Slam-winning prop Cyril Baille.
But things got worse for Toulouse with half an hour left. Irish winger Simon Zebo was late countered by Rory Arnold, who was shown a yellow card.
With Wallabies pinned Arnold, Carbery extended Munster’s lead to 10 points with just over 20 minutes of regulation time to play.
After Arnold’s return, Lebel found a void following a lineout and Zebo extravagantly bypassed.
Ramos kicked the simple conversion to silence the crowd and staged a tense 10-minute final with Toulouse trailing 24-21.
Winger Ramos then drew the teams to an equalizer with a penalty in the 75th minute before Healy missed a long-range shot with the clock in red, sending the game into two 10-minute overtime.
As the players began to tire and nerves, on and off the pitch, frayed, Healy and Ramos missed the drops before Healy sent a late attempt to send the match to penalties.
Healy missed his two efforts on either side of Murray’s failed attempt, sending Toulouse, flawless with his four kicks, to the fourth semifinal in as many years.
Elsewhere, last year’s runner-up La Rochelle will face Racing 92 or Sale Sharks for a place in the final, having passed Montpellier 31-19 when former New Zealand full-back Victor Vito scored his first try of the season.
The Sharks will head to Paris on Sunday with England flanker Ben Curry making his first Six Nations debut.