One of five Brazilian teams in the last 16, Gremio were reduced to 10 men in the 34th minute after referee Nestor Pitana sent striker Borges off for elbowing defender David Henriquez in the face at the Olimpico in Porto Alegre.
Six minutes before the red-card incident, Lucas Pratto raced onto a pass from Marcelo Canete and hit a right-footed shot low past goalkeeper Marcelo to give the Chilean champions a 1-0 lead.
The Brazilian side, champions in 1983 and 1995, hit back just before the hour when midfielder Douglas struck a left-footed shot from 30 metres into the top right-hand corner of Paulo Garces's net.
"We won because we managed to decipher the match before playing it... we took a big step, that gives us hopes," Catolica's coach Juan Antonio Pizzi told reporters.
At Velez Sarsfield's Fortin (fortress), strikers turned providers as Santiago Silva then Juan Manuel Martinez laid on the goals for midfielder Augusto Fernandez in the opening 10 minutes to give the Argentine's a 3-0 win over LDU Quito in Buenos Aires.
Silva crossed from the left in the seventh minute and Fernandez ghosted in at the far post to hit the ball first time into Alexander Dominguez's net.
