The second seeded Indo-Slovak pair fought hard for a 7-6 (5) 7-5 win against the Spanish-Czech combo in an hour and 23 minutes in the opening round of the clay court Grand Slam event.
Bopanna and Katarina are now up against Zimbabwe's Cara Black and Robert Farah from Colombia.
They converted four of the five breakpoints and fired eight aces to two of their rivals.
Sania Mirza is already in the pre-quarterfinals with Romanian partner Horia Tecau. If both Bopanna and Sania can manage to win the next matches, they will clash in the semifinals, which would mean that at least one Indian will fight for title.
Bopanna has never won a Grand Slam while Sania has two mixed doubles trophies in her cabinet.