Brendon Santalab's 85th-minute strike earned the A-League grand final losers a 3-3 draw on aggregate against the J.League champions.
The Australian side's hopes were left hanging by a thread after conceding late in Japan to trail by two goals and that first-leg deficit remained until the second half on Wednesday.
But two excellent strikes after the interval got the job done for Tony Popovic's men as Shannon Cole's leveller and Santalab's powerful volley secured a last-eight spot in Shinji Ono's last game for the club.
The Japan star is returning to his home country but signed off with a fond farewell at Pirtek Stadium.
Last season's losing finalists Seoul also progressed on away goals despite a 2-1 second-leg loss at home to Kawasaki Frontale.
That result left the aggregate score tied at 4-4, with Seoul having scored three times in Japan.
The South Koreans looked to be heading for a far more comfortable margin of victory when Sergio Escudero gave them an eighth-minute lead, but Yu Kobayashi levelled before the break.
Yasuhito Morishima then scored in stoppage time but it was too little, too late for the visitors.
Elsewhere, Al Sadd followed up their goalless home draw against Iranian outfit Foolad with a 2-2 result on the road to go through, while Al Hilal prevailed 4-0 on aggregate after a 3-0 second-leg triumph versus Bunyodkor.
