Al Nassr overturned a 1-0 first-leg deficit to win 4-3 on Monday but with the contest ending 4-4 on aggregate, the players headed into a shootout in which AlAin prevailed.
Al Nassr's foreign imports Miroslav Brozovic, Alex Telles and Otavio all failed to score from the spot as the side from the United Arab Emirates advanced to the semi-finals, where they will face either Al Hilal or Al Ittihad - both from Saudi Arabia - next month.
Al Ain goalkeeper Khalid Eisa made amends for a disappointing display when he saved Brozovic's opening penalty and, with Soufiane Rahimi, Kaku and Sultan Al Shamsi all converting, Otavio's miss meant Al Nassr were eliminated.
The shootout brought a dramatic end to a thrilling clash at Al-Awwal Park that featured seven goals and a red card, with Al Ain building on their first-leg lead during the opening 45 minutes.
Rahimi, scorer of Al Ain's first-leg winner, put the visitors in control with goals in the 28th and 45th minutes but Abdulrahman Ghareeb's strike five minutes into injury time kept Al Nassr's hopes alive.
Otavio's low drive was redirected into his own goal by Khaled Eisa six minutes after the restart and Alex Telles levelled the aggregate scores 18 minutes from time with a low free kick that flew through a crowd of players to beat Eisa.
Al Nassr's Ayman Yahya was sent off for a vicious two-footed lunge on Bandar Al-Ahbabi eight minutes into extra time and, a minute later, Al-Shamsi thought he had scored the winner when he capitalised on Raghid Najjar's handling error to poke home.
But Ronaldo scored from the penalty spot with two minutes remaining, after the Portuguese striker was taken down in the area by Saeed Jumaa, to take the game to a shootout.
Ronaldo was the only one of Al-Nassr's four penalty takers to successfully convert as Al Ain advanced to the last four for the first time since 2016.
In the eastern half of the draw, South Korean sides Jeonbuk Motors and Ulsan Hyundai will meet on Tuesday after sharing a 1-1 draw last week.
On Wednesday, Harry Kewell's Yokohama F Marinos side will hope to defend a 2-1 lead on home soil when they face Chinese Super League side Shandong Taishan.
