Ono, in his final game before returning to Japan, created two second-half goals -- one five minutes from time -- for a 2-0 win and 3-3 aggregate score, enough for the Wanderers to scrape through by virtue of their away goal in last week's 3-1 defeat.
The Wanderers looked headed for the exit but the match turned ten minutes after half-time, when Shannon Cole smashed in a volley after being teed up by Ono.
And following waves of attacks, the decisive goal came on 85 minutes when Brendon Santalab blasted home after more deft work from Ono, who will now leave for Consadole Sapporo. The Wanderers saw out the five minutes of stoppage time to preserve their advantage and go into the draw for the two-legged quarter-finals in August.
"I believe in this team and we believe in ourselves and that's why we have a good result tonight," Ono said afterwards.
"It's been a great year and I'm really pleased for the players," Popovic said, who played five seasons as a defender for J.League champions Sanfrecce. "It's great to send the players who are leaving out on a high and I'm just honoured to be head coach of this club. It's a very close unit. We understand the way football is, that players move on, but they gave everything they had for the club in their final game."
It is only the third time an Australian team has reached the AFC quarter-finals after Adelaide United in 2008 and 2012.
Late substitute Yasuhito Morishima curled a sumptuous shot into the net in stoppage time. But it was too late for Kawasaki to rescue the tie after they shipped two late goals in last week's first leg.
Meanwhile, 2011 champions Al Sadd edged Iran's Foolad Kouzestan on away goals to make the quarter-finals after both teams were locked in a 2-2 draw at the Ghadir Stadium in Ahwaz, Iran. After their goalless stalemate in Doha last week, Algerian Nadir Belhadj put the Qatari giants ahead in the 17th minute, and when Khalfan Ibrahim helped them consolidate with a 27th minute strike, Al Sadd looked well on course to a comfortable win.
However, Foolad hit back through a penalty converted by Luciano Chimba in the 77th minute and the Brazilian scored his second goal ten minutes later before Al Sadd held on grimly to secure the vital draw.
In Riyadh, Al Hilal thrashed Uzbekistan's Bunyodkor 3-0 to advance with a 4-0 aggregate. Veteran Yasser al-Qahtani put the Saudis ahead in the 20th minute and Nasser al-Shamrani and Salim al-Dawsari put the result beyond doubt with goals in the 47th and 58th minute.