Former Cardiff City goalkeeper Neil Etheridge saved a pair of spot-kicks to take 10-man Buriram United into the last eight for the second season in a row after an eventful contest against the Australians finished in a 0-0 draw.
That saw the two-legged clash end 1-1 on aggregate with Etheridge denying Ryan Teague and Aziz Behich to take Mark Jackson's team into the next round.
"Everything about the performance shows how together we are as a team," said Etheridge. "I'll take the plaudits for saving the penalties but for 100 minutes my team dug extremely deep to take it to the point where I was able to make those saves."
Buriram midfielder Robert Zulj was sent off in the 21st minute for stomping on a prostrate Harrison Shillington while Etheridge was fortunate not to be dismissed in the 96th minute when he appeared to aim a kick towards Max Caputo.
City defender German Ferreyra was sent off in the 119th minute following a tussle with Ruben Sanchez before Etheridge dived to his left to keep out penalties from both Teague and Behich, leaving Kenny Dougall to score the winner.
Meanwhile, Hotaka Nakamura's header confirmed Machida's progress after sharing a 0-0 draw with Gangwon in the first leg last week, with the club qualifying for the last eight in their debut campaign in the continental championship.
The right back scored in the 25th minute when he charged forward to meet Na Sang-ho's centre from the left, stooping to nod beyond goalkeeper Park Chung-hyo.
Machida and Buriram are the first teams to secure their places in the quarter-finals, which will be played in Jeddah on a centralised basis along with the tournament's semi-finals and final from April 16 to 25.
Japan's Vissel Kobe take a 1-0 lead into the second leg of their meeting with FC Seoul on Wednesday while Malaysia's Johor Darul Ta'zim will defend a 3-1 advantage against hosts Sanfrecce Hiroshima.
Matches in the last 16 in the western half of the draw have been postponed due to the ongoing conflict in the Middle East.