Robredo, seeded second, converted only two out of 11 break points on his way to victory. The Spaniard played a very solid game from the baseline and won 90 percent of his first serves.
Third-seeded Marin Cilic of Croatia also advanced, beating Dutchman Igor Sijsling 7-5, 6-3. It was Cilic's fourth victory over Sijsling in as many encounters and the Croatian was dominant from the start.
He took a 5-2 lead in the first set before Sijsling leveled for 5-5. Cilic then broke in the 12th game on his second set point.
Cilic, who won the tournament in 2012 and reached the 2011 final, broke again at 3-2 in the second set before easily finishing off the match.
"It is good that I won in two sets, conditions here are tough with humidity and heat," Cilic said. "I have adjusted well to the conditions, but winning as fast as possible is always recommended."