Ajaxís sensational Champions League run continued as teenage captain Matthijs de Ligtís goal eliminated Juventus and secured their place in the semi-finals.
Cristiano Ronaldo, a five-time winner of the tournament, headed the hosts in front from a first-half corner.
But Ajax battled level as Donny van de Beek controlled Hakim Ziyechís shot and slotted past Wojciech Szczesny.
Ziyech went close after the break before De Ligt, up from the back, scored a decisive, powerful header.
The away-goals rule left Juventus needing two in the remaining 23 minutes, but it could have been even more comfortable for the visitors in the closing stages with David Neres shooting wide and Ziyech flagged offside after whipping a smart shot into the top corner.
Ronaldo, who picked up a late yellow card for frustrated lunge at Joel Veltmans, stalked off the pitch at the final whistle, having been knocked out of the competition for the first time since Juventus beat his previous club Real Madrid in May 2015.
Meanwhile, as they did after their sensational away win over Real Madrid in the previous round, Ajaxís youthful side bounced in front of their raucous band of supporters and home fans streamed out the exits.
Ajax will face the winner of Manchester City and Tottenhamís quarter-final, which Spurs lead 1-0 before Wednesdayís second leg at Etihad Stadium.
Victory marks Ajaxís return to the last four of Europeís premier competition for the first time since a team containing Daley Blindís father Danny, Marc Overmars and Ronald de Boer were beaten in the 1997 semi-finals - by Juventus.
Without an automatic group-stage place for the Eredivisie, the current side started their Champions League campaign as 250-1 outsiders in Julyís qualifying rounds.
However, their attacking exuberance and unwavering belief in their ability to match the continentís best was summed up by De Ligt.
The 19-year-old captain was found wanting for Ronaldoís opener, unable to track the Portugueseís run through a packed penalty area and leaving him free for the 98th headed goal of his career.
However, after regaining his defensive composure, De Ligt completed his redemption from Ajaxís own set-piece, planting a downward header past a rooted Szczesny.
This season will be this Ajax sideís only shot at regaining the trophy they last won in 1995.
Manager Erik ten Hag has admitted De Ligt will leave at the end of the season, while team-mate and fellow teenager Frenkie de Jong has already agreed a summer move to Barcelona. Dangerous wide attacker David Neres, meanwhile, has been linked with a move to the Premier League.