Estudiantes crushed Cruzeiro 4-0 in the Libertadores Cup on Wednesday after the Brazilians arrived late for the match due to traffic problems.
San Lorenzo, the only one of the big five Argentine clubs never to have won the competition, were knocked out after losing 2-0 away to San Luis in Mexico, coach Miguel Russo resigning in the team hotel in the aftermath.
Cruzeiro stayed top of Group Five with 10 points from five games despite seeing their unbeaten record go up in smoke against the Argentines in La Plata.
The match kicked off 40 minutes late after Cruzeiro were forced to take an alternative route for the 60-kilometre journey with the main Buenos Aires-La Plata highway blocked.
Brazilian media said Cruzeiro still got caught in heavy traffic and took more than three hours for the journey.
Having rushed their warm-up, their problems continued when Juan Sebastian Veron scored a simple goal after six minutes and Gaston Fernandez added a brilliant second in the 32nd.
Cristian Sanchez Prette scored twice in three minutes in the second half as Estudiantes avenged a 3-0 defeat earlier in the group and moved within one point of their opponents.
San Lorenzo were eliminated after their fourth successive defeat left them bottom of Group Eight with three points.
Jesus Palacios and Jose Reyes took advantage of slack marking to head the goals while Omar Monjaraz (San Luis) and Andres Silvera (San Lorenzo) were sent off for fighting in the 45th minute.
Russo announced his resignation afterwards. "That's football," he told Argentine television in an interview.
Palmeiras, who lost their first two games in Group One, bounced back by winning 2-0 at Sport Recife in an all-Brazilian grudge match, Keirrison and Diego Souza scoring in each half
The match in Recife had been considered high-risk after a domestic game at the same venue last year in which Palmeiras' bus was pelted with missiles.
Palmeiras also complained that Sport fans let off fireworks outside their hotel the night before the game.
This time, Palmeiras stayed at a beach resort outside the city and there were no reports of trouble.
Chilean champions Colo Colo, who have six points, lead on goal difference from Sport while Palmeiras and defending champions LDU have three apiece.