Harlequins edged out formidable Bordeaux in a 12-try classic to reach the semi-finals of the Champions Cup for the very first time.
Quins produced a stunning upset away at a baking Stade Chaban-Delmas on Saturday to keep their hopes of European glory alive, winning by a single point, 42-41.
Either Top 14 contenders Toulouse or Premiership rivals Exeter now await in the last four, with that quarter-final contest taking place on Sunday.
Quins full-back Tyrone Green scored the clincher, although Bordeaux still had a chance to win it, but skipper Maxime Lucu missed the conversion of Madosh Tambwe's 76th-minute try.
It was a spectacular triumph, with scrum-half Will Porter scoring two tries, while there was also a penalty try and touchdowns for flanker Will Evans and number eight Alex Dombrandt.
Marcus Smith kicked five conversions, and Bordeaux were ultimately thwarted despite tries from Lucu, Romain Buros, Nicolas Depoortere, Louis Bielle-Biarrey and Tambwe's double, with Lucu landing four conversions and a penalty.
Quins made a blistering start in 30-degree heat, stunning their hosts by scoring the game's opening try after just three minutes.
England flanker Chandler Cunningham-South did the hard yards on his return to action from injury, punching holes in Bordeaux's defence, before centre Andre Esterhuizen's touchline break saw him find Porter with a scoring pass.
Smith added the conversion and things got quickly got even better for Quins when referee Andrea Piardi awarded them a penalty try after Smith's pass to an unmarked Louis Lynagh was deliberately knocked on by fly-half Mateo Garcia, who received a yellow card.
The game's first water break also saw umbrellas brought on to protect Bordeaux players from the sun and after being suitably refreshed, they attacked from a close-range lineout before skipper Lucu applied an emphatic finish.
Bordeaux had gone up a gear and they struck again six minutes later when a sweeping attack inside Quins' half was rounded off by Buros, with Lucu's conversion narrowing the gap to two points.
It was a pulsating contest and Quins conjured a memorable try 10 minutes before half-time just when it looked as though Bordeaux had grasped the initiative.
Wing Cadan Murley spun in and out of Bordeaux tackles before finding Dombrandt, whose inside ball to Porter saw the scrum-half kick ahead and regather for his second touchdown. Smith's conversion took Quins past 20 points.
And a first-half masterclass concluded from Quins when two shows of their scrum dominance was followed by a driven line-out and Evans dived over for their fourth try, with Smith converting for a 28-12 interval advantage.
Bordeaux knew they had to score first in the second half and it took them barely three minutes as Depoortere claimed a superb solo try, collecting a pass just inches off the ground before brushing aside Quins defenders.
Lucu converted and Bordeaux were rapidly establishing momentum as a long-range penalty from the captain left them six points adrift midway through the third quarter.
Quins, though, knocked Bordeaux backwards once again, and Dombrandt scored their fifth try approaching the hour mark, with Smith's conversion making it 35-22, only for Bielle-Biarrey to touch down after Quins' defence was splintered.
And when Tambwe sprinted over with 15 minutes remaining - Lucu's conversion put Bordeaux ahead for the first time - the momentum appeared to have shifted, especially when Quins hooker Sam Riley lost control of the ball while going over the home line following a forward drive.
But Green then struck to revive hopes of a famous win and hopes were further raised when Lucu missed the conversion of Tambwe's second try before they ran down the clock and could start to celebrate an astounding success.
