Few gave Juve a chance of reaching the last 16 after a horror show in Istanbul last week left the Italians trailing 5-2 and needing a near-miracle to get through to the next round.
But elimination was especially painful as a superb performance and goals from Manuel Locatelli, Federico Gatti and Weston McKennie took the tie to extra time in a cacophony of noise.
Victor Osimhen and Baris Yilmaz netted in that additional period to send Juve out, leaving captain Manuel Locatelli admitting: "I feel like crying."
"All I know is that we put our souls into that match, we gave everything we had," said Locatelli.
Juve were applauded off by their supporters after a display which will boost them in their bid to qualify for next season's edition of the Champions League.