"I played a very, very solid match," said Granoller after his win. "I played with high percentage of first serve. I know he's very dangerous. He [has] great hands, but I think I played a solid match and he [made] a few mistakes that helped me."
The No. 112-ranked Granollers, who won the tournament in 2008, was not bothered by the unpredictable Aussie, as he needed just 47 minutes to take care of the Aussie.
"Well, I have to focus on my game, my work. I was trying to play point, point by point, every point as good as I can. And only focus on my self."
The Spaniard has won more tour-level singles matches this week than he has all season. He was 1-5 before entering Houston—his lone win was in the Montpellier first round against Ivo Karlovic.
Up next for 32-yer-old Granollers is either No. 4-seeded Reilly Opelka or 20-year-old Casper Ruud, who's dad is a former Houston champion.