Younis struck three minutes into time added on to earn the A-League side a fourth win in the league phase, with the victory guaranteeing Aurelio Vidmar's side a top-eight finish.
"Today was about the team, it's the first time in Melbourne City's history to get this far," said Younis, who is on loan from Danish side Brondby.
"I'm proud of the boys, proud of the team to go this far and today will be in my memory forever."
Melbourne City took the lead through a Max Caputo header in the 36th minute but Darijan Bojanic levelled the scores from distance with 10 minutes remaining.
However, Younis hit the winner when Kavian Rahmani's pass was not cleared and the 20-year-old volleyed in with his left.
The win lifts City into fourth place on 13 points from seven matches and in the 12-team table, trailing Japanese trio Vissel Kobe, Machida Zelvia and Sanfrecce Hiroshima, who all confirmed their progress on Tuesday.
The first eight finishers in the league phase in both east and west Asia advance to the last 16, which will be played on a home-and-away basis in March. The quarter-finals, semis and final will be held in Saudi Arabia in April.
The last round of group matches are next week, with six clubs vying for four remaining berths in the knockout rounds.
Shanghai Port will not be among those progressing after Kevin Muscat's side were held to a 0-0 draw in South Korea by Gangwon FC, with that result leaving the Chinese champions bottom of the standings, five points adrift of eighth place.