River were trailing 3-0 after less than 20 minutes and 4-1 at halftime on their way to their first defeat in the competition.
Jonathan Santana put San Lorenzo ahead after 27 seconds when Gonzalo Bergessio pulled the ball back from the byline. Adrian Gonzalez was also on target with a fifth minute free kick.
Jonathan Bottinelli added the third in the 17th minute after a series of rebounds in the area and, although Diego Buonanotte pulled one back for River, Bergessio netted a fourth on the stroke of halftime.
Andres Silvera completed the rout in the 57th minute and the only unhappy note for Miguel Angel Russo's team was a red card for Alejandro Gomez in the 80th minute for a bad tackle on Oscar Ahumada.
"It was an odd game," said River coach Nestor Gorosito, who is trying to restore his team's credibility after they finished bottom of the Apertura championship in the second half of last year.
"Every time they attacked, they scored a goal. When it was 3-1, we were close to a second but they scored a fourth."
Boca Juniors striker Martin Palermo scored his first goal since returning from a six-month injury lay-off to set his team on the way to a 3-1 win over Huracan.
Palermo, a cult figure with the Boca crowd, scored a typically opportunist effort in the 69th minute.
Luciano Figueroa added two more in the last 10 minutes and Eduardo Dominguez replied for Huracan.
Arsenal went top by beating nine-man Estudiantes 3-1 with first-half goals from Jossimar Mosquera, Luciano Leguizamon and Javier Yacuzzi.
Enzo Perez replied for Estudiantes who had Agustin Alayes sent off in the 47th minute and Diego Galvan in the 73rd.
Arsenal have nine points from four games and lead Gimnasia-La Plata and Lanus on goal difference.
