Federer defeated Roberto Bautista Agut of Spain 6-3, 2-6, 6-4, a day after being taken the distance by Daniil Medvedev of Russian Federation. Nevertheless, the top seed insisted he was content with how he's playing.
Bautista Agut, a finalist here in 2016, finally offered Federer an opening to take control by surrendering his serve in the ninth game of the third set.
"I was telling myself, particularly tonight I can not do this (lose) because they were there, but I don't know how much I draw from that, quite honestly". "Since Hamburg I got a lot of confidence and that helped me in Beijing".
On Sunday, Basilashvili upset fourth-seeded Juan Martin del Potro in the final in Beijing.
However, the Swiss is a great champion for a reason and he found a late surge to rip the match away from his opponent to set up a quarter-final clash with Kei Nishikori.
But the Spaniard earned a piece of personal history after that, winning the second set - the first time he had taken a set against the Swiss maestro.
Australian Matthew Ebden upset sixth-seeded Dominic Thiem 6-4, 6-7 (8), 7-6 (4) in a almost three-hour match.
The Spaniard folded at the end of a 27-shot rally to surrender the first break of the match to the world No. 2, who soon wrapped up the first set.
Wimbledon and U.S. Open champion Novak Djokovic exacted revenge over Italian Marco Cecchinato with a 6-4 6-0 victory.
A Masters event is a level below a Grand Slam, but Djokovic was rapt to crush Cecchinato.
"I hope it's going to help me that I played against Medvedev and also Bautista Agut, two really good baseliners".
Anderson ousted 10th-seeded Stefanos Tsitsipas of Greece 6-4, 7-6 (1).
Briton Kyle Edmund, who moved to a career-high ranking of 14 this week, continued his impressive run in Asia with a 7-5 6-3 win over Serbia's Filip Krajinovic.