River won 1-0 at San Lorenzo last month and a cagey stalemate in the return was enough to see them through.
San Lorenzo pushed hard but were restricted to long-range attempts in the first half, all of them snaffled safely by home goalkeeper Marcelo Barovero.
Barovero was beaten shortly after the restart but Leandro Navarro's wonderful free-kick crashed off the bar and away to safety.
Man of the match Barovero came to River's rescue late on when defender Walter Kannemann ran through on a one-on-one but could not find the net.
San Lorenzo's frustration at failing to conjure up a goal spilled over in injury time when Pablo Alvarado aimed a head-butt at Carlos Carbonero and was sent-off.
"We deserved to go through," insisted River's Cristian Ledesma. "We played hard against a very tough rival. There was only one goal difference between the sides and it was ours."
San Lorenzo's Leandro Romagnoli saw it differently and bemoaned River's negative tactics.
"River never tried to play, it was a bad match and not fair on us as I believe we did a better job," he said.
"We had a lot of scoring opportunities over the two legs and them only one."
In the next round, River will face Ecuador's Liga de Loja.