Having squandered five break point opportunities, Federer finally broke Bautista Agut to 15 in the 10th game to clinch the 42-minute first set. The Swiss lost just five service points.
Federer took a 3-0 lead in the second set en route to his 58th match win of the season, which includes three ATP World Tour titles.
"I think I definitely played better," said Federer, in comparison to his opening win over Leonardo Mayer on Wednesday. "I had a better understanding of how the balls are reacting, the court is playing, and just conditions in general at night.
"I definitely think he let me play a bit more from the baseline, whereas Mayer really took big cuts at the ball which made it really difficult for me to control the back of the court. I think I was just overall striking the ball better. I'm glad I got a straight set win tonight."
Federer will next face Julien Benneteau. The pair has met on seven occasions, with Federer leading their ATP Head2Head series 5-2. Benneteau beat Federer in their last hard-court meeting, 6-3, 7-5, in February 2013 at the ABN AMRO World Tennis Tournament.
"I think he plays well against the better players usually," said Federer. "I've struggled against him in the past, mostly indoors really, then that one time at Wimbledon, which was also played indoors. So it will be interesting to see how he plays here because he has played very consistent, very solid from what I've seen."
Benneteau, who beat World No. 10 Grigor Dimitrov in the Shanghai third round, defeated Jack Sock 6-3, 6-4 in 71 minutes for a quarter-final berth.
Date: 9th October 2014, Source: ATP
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