Goals from Leonardo Pisculichi, Teofilo Gutierrez and Lucas Boye cancelled out Mauro Matos' opener as River prevailed 3-1 against the Copa Libertadores title holders on Sunday.
San Lorenzo's woes were compounded after they were forced to play the final 12 minutes a man down - and were down to nine with four minutes remaining - as Juan Mercier and Mauro Cetto were sent off at the Estadio Pedro Bidegain.
River opened up a one-point lead atop the summit with 13 points from five matches after Velez Sarsfield's perfect start to the season came to an end as they lost 3-1 at Boca Juniors.
San Lorenzo - second from bottom in the table - made a dream start to proceedings in front of their own fans when Matos opened the scoring after six minutes.
River were caught on the break as Hector Villalba squared the ball to an unmarked Matos inside the penalty area and the veteran striker made no mistake from close range.
The home side were pegged back just six minutes later following Pisculichi's half-volley from outside the box.
It got better for River after half-time as they added two unanswered goals through Gutierrez and Boye.
Colombian attacker Gutierrez made it four goals in three games when he tapped the ball home from inside the six-yard box a minute shy of the hour-mark.
And one minute after Mercier was shown a straight red card, Boye headed home to double the visitors advantage.
To make matters worse for San Lorenzo, Cetto was shown a second yellow card with four minutes remaining.
It was an identical scoreline at the Estadio Alberto Jacinto Armando - commonly known as La Bombonera - on Monday as Boca made a winning start under new coach Rodolfo Arruabarrena.
Arruabarrena - winner of four trophies with the club during his playing days - was named coach of Boca after Carlos Bianchi was sacked on Thursday and it appeared to work wonders as they defeated Velez courtesy of second-half goals from Daniel Diaz, Cesar Meli and Andres Chavez.
Velez's slip up opened the door for Newell's Old Boys, who closed to within a point of second spot thanks to a 1-0 win at home to Estudiantes on Saturday.
Mauricio Tevez's 71st-minute strike proved the difference as Newell's preserved their unbeaten start to the season.
In other results, fourth-placed Rosario Central accounted for lowly Defensa y Justicia 3-1.
Rosario are level on nine points with Arsenal, Independiente and Racing Club.
Arsenal edged 10-man Banfield 1-0, while Independiente upstaged Racing 2-1 with all three goals scored during the first half.
Belgrano notched their first win of the season, routing Atletico Rafaela 3-0.
Gimnasia La Plata were also winners for the first time after Jorge Rojas and Javier Mendoza inspired them to a 2-0 victory over Godoy Cruz.
Meanwhile, Tigres and basement club Quilmes played out a goalless draw.
