The 20-year-old winger, who's on loan from Danish Superliga club Brondby volleyed home a superb clincher three minutes into time added on, earning Aurelio Vidmar's side a fourth victory in the league phase to confirm their progress with a guaranteed top-eight finish.
"Today was about the team, it's the first time in Melbourne City's history to get this far," said the thrilled Younis, who'd previously played at Western Sydney Wanderers.
"I'm proud of the boys, proud of the team to go this far and today will be in my memory forever."
City had taken the lead through a Max Caputo header in the 36th minute from a pinpoint Younis cross, but Darijan Bojanic had made it a nervy finish when he equalised with a shot from distance with 10 minutes remaining.
But when the Ulsan defence failed to clear their ranks in the dying seconds, the ball fell to Younis, whose crisp left-foot volley ensured folk hero status with the City faithful.
The victory put City fourth in the 12-team east table on 13 points from seven matches, behind the three Japanese clubs, Vissel Kobe, Machida Zelvia and Sanfrecce Hiroshima, who had all sealed their progress 24 hours earlier.
City will now be in the last-16, with eight sides also qualifying from the west league, earning them a home-and-away tie next month. The quarter-finals, semis and final will then all be held in Saudi Arabia in April.
The final round of group matches are next week, with six clubs vying for four remaining berths in the knockout rounds, but Australian boss Kevin Muscat's Chinese Super League champions Shanghai Port failed to make it after a 0-0 draw against Gangwon FC in South Korea.
Muscat's side are now bottom of the league standings, five points adrift of eighth place.
In the west group, Algeria international Houssem Aouar scored a hat-trick as Al-Ittihad routed Qatar's Al-Gharafa 7-0, a result that ensured the two-time champions joined their fellow Saudi sides Al-Ahli and Al-Hilal in the round-of-16.
Meanwhile, Cristiano Ronaldo missed his third consecutive game for his Saudi side Al-Nassr as they beat Turkmenistan's Arkadag FC 1-0 in the first leg of the round-of-16 in the AFC Champions League Two.
Ronaldo has been absent amid reports that he's unhappy with how the club is being run by Saudi Arabia's Public Investment Fund.
With agencies
