Second seed was in scintillating form to thrash Kyrgios while sixth seed Djokovic was too strong for Gasquet
Federer and Djokovic dominate to edge closer to US Open quarter-final showdown
Five-time champion Roger Federer found a new way to amaze on Saturday as he reached the US Open last 16 with a 6-4, 6-1, 7-5 victory over Nick Kyrgios.
The second-seeded Swiss withstood an early onslaught from the unpredictable Australian, firing 51 winners that included an unlikely forehand flicked around the net post that Kyrgios couldn't believe.
"Definitely a bit of luck and good feet," Federer said of the shot that had Kyrgios wide-eyed at the net.
Federer had the luxury of a two-set lead when the duo's most entertaining exchanges thrilled the Arthur Ashe Stadium crowd.
Things would have been much different if Kyrgios could have converted one of four break points in the seventh game of the opening set. But Federer escaped, breaking Kyrgios to pocket the first set and dominating the second.
"He's an unbelievable frontrunner," Kyrgios said. "When he gets in front, there's not much you can do."
Federer will be seeking a 13th appearance in the US Open quarter-finals when he plays Australian John Millman, who reached the last 16 of a major for the first time with a 6-4, 4-6, 6-1, 6-3 victory over Kazakhstan's Mikhail Kukushkin.
If he makes it past Millman, Federer could find Wimbledon champion Novak Djokovic waiting in the last eight.
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Djokovic, winner of US Open titles in 2011 and 2015, extended his dominance over Richard Gasquet with a 6-2, 6-3, 6-3 victory in front of a rowdy night crowd on Ashe.
"It was the best match of the week so far without a doubt, and one of the best performances of the hardcourt season after Wimbledon," said Djokovic, who warmed up for Flushing Meadows by beating Federer in the Cincinnati Masters final.
Djokovic saved all five break points he faced to book a meeting with Joao Sousa of Portugal, a 7-6, 4-6, 7-6, 7-6 winner over France's Lucas Pouille.
Also through to the last 16 is 2014 finalist Kei Nishikori after the Japanese No 1 defeated Argentina's Diego Schwartzman 6-4, 6-4, 5-7, 6-1.
Nishikori will take on Philipp Kohlschreiber after the German produced the shock of the day by beating compatriot and fourth seed Alexander Zverev 6-7, 6-4, 6-1, 6-3.
Belgian 10th seed David Goffin had few problems in his third round match against Germany's Jan-Lennard Struff, emerging victorious 6-4, 6-1, 7-6. Goffin will take on 2014 champion Marin Cilic after the seventh seeded Croatian won a marathon match against Australian teenager Alex De Minaur.
Cilic defeated 19-year-old De Minaur 4-6, 3-6, 6-3, 6-4, 7-5 in the second ever latest finish at the tournament.
The Croatian needed eight match points to defeat the world No 45 in a four-hour epic which ended at 2.22am local time (10.22am UAE), just four minutes short of the record for the latest finish.