Li Shenglong's fantastic diving header threw SIPG into the second round after collecting Civanildo Souza (Hulk)'s corner kick.
The Curitiba-based side top the Group C standings with six points from three matches, ahead of Chile's Colo-Colo on goal difference. Jorge Wilstermann are third with three points.
Stage One involves 32 groups of four players, with the player who tops each group progressing to Stage Two.
"I'm always proud to wear my colors. Thank you, Pumas, for trusting me and being my support," Talavera, who has been capped 28 times, said in a Twitter post.
"We had two big chances in the first half but Dortmund were more effective and clinical in front of the target today," Monchengladbach head coach Rose said.
Veteran striker Roberto Soldado put Granada ahead after just four minutes with a left-foot volley from Yangel Herrera's cross and the Spanish side's nerves were well and truly calmed six minutes later, when Kenedy doubled their lead.
In Group D, Al-Nassr FC of Saudi Arabia continued their charge towards the round of 16 with a 2-0 win over Iran's Sepahan thanks to a brace from Abderazzaq Hamdallah.
In Chilean capital Santiago, Colo-Colo defeated Uruguay's Penarol 2-1 while Brazil's Santos were held to a goalless home draw by Paraguayan side Olimpia. Enditem
The 33-year-old Serb now faces a semifinal against Casper Ruud of Norway, who beat fourth seed Matteo Berrettini of Italy 4-6, 6-3, 7-6 (5).
In another match of group C, Persepolis FC edged Al Taawoun 1-0 as the Iraqi midfielder Bashar Resan scored the match's only goal from the penalty spot to take Iranian side to the top of the group with seven points.
Getafe's Matchday 1 fixture against Real Madrid was pushed back to a later date due to Real Madrid's European commitments in the summer and Osasuna may feel that after beating Cadiz last week they have a competitive edge against Pepe Bordalas' always tough-to-beat side.