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Ajax's sensational Champions League run continued as teenage captain Matthijs de Ligt's 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 Ziyech's 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 a 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, Ajax's 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 Tottenham's quarter-final, which Spurs lead 1-0 before Wednesday's second leg at Etihad Stadium.
Ajax celebrated long and loud at the final whistle
Victory marks Ajax's return to the last four of Europe's premier competition for the first time since a team containing Daley Blind's 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 July's qualifying rounds.
However, their attacking exuberance and unwavering belief in their ability to match the continent's best was summed up by De Ligt.
The 19-year-old captain was found wanting for Ronaldo's opener, unable to track the Portuguese's run through a packed penalty area and leaving him free for the 98th headed goal of his career.
Ajax's social media team made light of the rumours of bids for their leading players in the wake of their win. Marc Overmars, a member of the club's 1995 Champions League winning side, is the current director of fooball.
However, after regaining his defensive composure, De Ligt completed his redemption from Ajax's own set-piece, planting a downward header past a rooted Szczesny.
This season will be this Ajax side's 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 Frenkie de Jong, 21, has already agreed a summer move to Barcelona. Dangerous wide attacker David Neres, meanwhile, has been linked with a move to the Premier League.
Ronaldo has scored 126 goals in the Champions League, with 65 of those coming in the knockout stages - both the most of any player in competition history.
Ronaldo, recruited at a cost of £99.2m in the summer, was intended to provide the final piece of Champions League-winning know-how for a Juventus side that had lost two finals in the previous four seasons.
A second-leg hat-trick dragged his side to victory over Atletico Madrid in the last 16, but his dreams of matching former Ajax, Real Madrid and AC Milan midfielder Clarence Seedorf by lifting the trophy with a third different club were wrecked by Ajax's collective brilliance.
Instead, he will be absent from the last four for the first time since 2010.
Funds allowing, manager Massimiliano Allegri may contemplate more additions to his squad this summer to try to add continental success to their domestic dominance.
Morocco international Ziyech was a constant bundle of energy down the right with four key passes and seven crosses - more than any other Ajax player
