Guillermo Barros Schelotto's Lanus side claimed a 2-1 victory at home to Santos Laguna in the first leg of their round-of-16 tie.
Carlos Quintero put the visiting Mexicans ahead just before the hour-mark, only for Argentina's Lanus to respond.
Facundo Monteseirin levelled and Matias Martinez was the hero with a dramatic winner in the dying seconds.
Quintero fired Pedro Caixinha's Santos Laguna into a 58th-minute lead, controlling a throw-in before smashing a finish into the roof of the net from a tight angle.
Lanus responded eight minutes later through Monteseirin, who volleyed home a Diego Gonzalez pass from inside the area.
There was to be late drama and, much to the delight of the home fans, it benefitted Lanus.
A set-piece whipped in from the right went uncleared and Martinez headed in the loose ball to give his side a 95th-minute winner.
Cruzeiro also left it late, but their 94th-minute goal from Miguel Samudio was an equaliser to give them a 1-1 draw at home to Cerro Porteno.
The Paraguayans took a 32nd-minute lead as Angel Romero tapped in from close range, and they looked headed for victory.
With just 20 seconds remaining of additional time, Samudio struck after a scramble in the area, with his effort going through a sea of bodies.
In Mexico, Leon came from behind to draw 2-2 at home to Bolivia's Bolivar.
Luis Montes and Juanmi Callejon traded first-half goals before the visitors went ahead through Juan Carlos Arce's 71st-minute goal.
When Juan Gonzalez saw red for Leon, the hosts looked certain to go into the second leg with a one-goal deficit.
But Mauro Boselli netted with four minutes remaining to see Leon to an unlikely draw.
