Cristiano Ronaldo had given the hosts the lead in the Champions League quarter-final second leg, with Juve moving 2-1 in front on aggregate and appearing on course for a place in the semi-finals.
The Dutch side were having none of it, however, as goals in reply by Donny van de Beek and Matthijs de Ligt, who has been linked with a move to Juve, secured an incredible 3-2 aggregate win for Ajax to send them through.
Having already knocked out Real Madrid at the last-16 stage, Erik ten Hag and his players can now look forward to a semi-final meeting with either Tottenham or Manchester City having dumped out Serie A champions-elect Juve.
And the players were understandably joyous after the final whistle, with the celebrations continuing in the dressing room as the club reached the last four of the competition for the first time since 1997.
Goalkeeper Onana posted a clip on his Twitter page showing the Ajax players dancing away, poking fun at Klaas-Jan Huntelaar and his selection of moves in the process. The caption read: "That Semi-Final feeling! Huntelaar what are those moves bro?!"
He added: "This amazing journey isn’t ending just yet! Very proud of this team and all your support. One last thing... Ajax ARE IN THE SEMI-FINALS!"
Daley Blind also took to social media to celebrate the win, writing: "Proud of this team!! What a Night!"
Ajax have earned rave reviews for their performances in Europe's premier club competition this season, with Barcelona legend Carles Puyol writing on Twitter after the Juve triumph: "Congratulations Ajax, you are amazing guys."
Atletico Madrid forward Antoine Griezmann has also been hugely impressed by what he's seen and he wrote in the aftermath of Tuesday night's result: "FOOTBALL! Bravo Ajax."
It's back to league matters for the Amsterdam club next, however, as they face Groningen in Eredivisie.
Ten Hag's side are currently joint top of the table, alongside PSV, and are also in the KNVB Cup final, where they will face Willem II.