A goal up after winning February's first leg, French side Lyon will face Manchester City at the final tournament in Lisbon after drawing 2-2 on aggregate and going through on away goals.
Olympique Lyonnais has qualified for the quarter-finals of the Champions League on Friday despite losing 2-1 to Juventus in Turin.
Cristiano Ronaldo scored a brace, including an unstoppable long-range goal, to give Juventus a win over Lyon but it was not enough as the French side reached the quarter-finals on away goals.
After both sides converted contentious penalties in the first half, Ronaldo struck from out of the blue on the hour but Lyon clung on for a 2-2 aggregate draw which sent them to next week's Final Eight tournament in Lisbon. They will meet Manchester City in a one-legged quarter-final.
The defeat left Juventus coach Maurizio Sarri in an uncomfortable position as the Champions League title eluded the Turin side for another season.
Reach away from Champions League trophy
Although Juventus have won Serie A for nine seasons in a row, they have not been able to get their hands on the Champions League trophy since 1996 when they won it for the second time.
Despite continuing the domestic run, Sarri failed to give Juventus the flamboyant touch the club had been looking for as well as missing out on their main goal.
It was an uphill struggle for Juve from the moment they conceded an away goal in the 12th minute, albeit in controversial circumstances.
Rodrigo Bentancur appeared to get the ball cleanly off Houssem Aouar but referee Felix Zwayer pointed to the spot and chose not to look at the incident on the pitchside monitor.
Dempay converted with a cheeky Panenka-style penalty which sent Wojciech Szczesny the wrong way.
Ronaldo saw a free-kick palmed away by Anthony Lopes but it was another controversial penalty which provided the hosts with their equaliser.
Miralem Pjanic's free-kick struck Depay's elbow in the wall and, although his arm was close to his body, the referee gave another penalty, again without consulting the pitchside monitor.
Juventus seemed to be making little progress after halftime until Ronaldo found space for a shot and blasted the ball past Lopes from 25 metres on the hour.
After that, it became almost a Ronaldo one-man show as he set up a chance which Gonzalo Higuain headed over, then headed over himself and drilled a free-kick into the wall. But even he could not find the winner.
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