"He had the advantage for a set and a half but I got my serve going and that was the key to it I think. I am a little bit tired but I am in the third round now and I am looking forward to it."
Robredo also had to pull out all the stops to beat fellow Spaniard Juan Carlos Ferrero 7-6, 4-6, 6-4.
Andre Agassi also continued to confound those who believe his 18-year career is almost over by beating former Australian Open champion Thomas Johansson to reach the last 16.
The American won 6-1, 3-6, 6-1 in a match twice interrupted by rain.
"You get more experienced at not getting overly concerned about things you can't control," the 34-year-old said. "The good news is that both guys have to deal with it."
It was only the second time Agassi had won two successive matches since March and it earned him a third round match against Juan Ignacio Chela, the 17th seed from Argentina.
"Two matches in a row is good for me but it's not good that it's good for me," Agassi said. "But it does feel good. Hopefully I am not too far away from feeling really good."
In the same half of the draw, defending champion Andy Roddick beat Germany's Nicolas Kiefer for the third time in 10 days.
Meanwhile, Wimbledon champion Maria Sharapova had little difficulty in her first match at the Montreal Cup, defeating Kristina Brandi, of Puerto Rico, 6-1, 6-4.
However, fourth-seeded Elena Dementieva and Russian compatriot Nadia Petrova, the eighth seed, were second-round losers.
Sharapova, 17, was challenged briefly in the second set but quickly recovered and put the match away with her dominating backhand and solid groundstrokes.
"She definitely picked up her game in the second set," the sixthseeded Sharapova said.
"I never expect to play my best tennis in my first match, but I did everything I had to do to win."
Dementieva lost to Argentina's Gisela Dulko 6-1, 6-4 and Petrova was defeated 6-4, 6-7, 7-5 by fellow Russian Elena Likhovtseva.
