The ninth-ranked Serb now faces Nicolas Almagro, a late replacement for Rafael Nadal who pulled out of the tournament with a stomach bug.
"It's not every day that you get to play a Grand Slam champion and an Olympic gold medalist," Tipsarevic said.
"I know it's an early season tournament but I can tell you that the six of us take this very seriously. I knew I could beat Andy as I have beaten him before. He's a totally different animal now as he won a Grand Slam and Olympic gold so beating him here has given me confidence. Both of us have very similar games so it's great to come out on top."
