A late goal from Lekhwiya's Ismaeel Mohammad ended Al Sadd's hopes of a third AFC Champions League title.
Just five days after their capture of World Cup winner Xavi was confirmed, Al Sadd suffered disappointment as they exited the AFC Champions League in the last 16 at Lekhwiya.
Trailing 2-1 from the first leg, Al Sadd looked set to force extra time as they came from behind to lead 2-1 on the night.
Youssef Msakni put Michael Laudrup's Lekhwiya ahead in the 13th minute but, after the hosts were reduced to 10 men when defender Ahmed Yasser was dismissed in the 34th minute, Muriqui and Ali Assadalla turned things around for Al Sadd.
However, there was a final twist in the tale as Ismaeel Mohammad netted seven minutes from time for Lekhwiya to give them a 4-3 aggregate win.
Three-time champions Suwon Bluewings also suffered elimination on away goals despite beating Kashiwa Reysol 2-1.
Kashiwa won the first leg 3-2 and secured their place in the quarter-finals thanks to midfielder Yusuke Kobayashi's 65th-minute strike, which proved to be enough after Jong Tae-se and Koo Ja-royng had given Suwon a 4-3 aggregate lead.
While Suwon's hopes came to an end, their K-League rivals Jeonbuk Motors progressed 2-1 on aggregate over Beijing Guoan courtesy of a 1-0 success in the Chinese capital.
Brazilian forward Edu scored the decisive goal in the 72nd minute before Zhou Ting was sent off for the hosts in stoppage time
Al Hilal cruised into the last eight with a 3-0 win home win against Persepolis, who had Mehdi Taremi sent off late on, ensuring a 3-1 victory on aggregate.