Seventh seed Kevin Anderson took down Nicolas Kicker 7-6 (1), 7-6 (3) and South Korea's Chung Hyeon beat Tomas Berdych 6-4, 6-4.
Meanwhile, Federer progressed to Round of 32 of the ongoing ATP Masters event in California.
Federer cruised to a 3-0 lead in the second and closed out the win in 58 minutes.
Federer, who had looked slightly off his game in his rain-disrupted third-round match against Federico Delbonis, was his dominant self yesterday, winning 89 per cent of his first service points while cracking six aces to just one double fault.
Federer improved to 65-5 since returning from a left knee injury past year with his third-round victory in a rare day match Monday.
"Very weird. I completely lost rhythm", admitted the Serb.
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With his triumph on Monday, Federer, victor of the 2018 Australian Open (20th Grand Slam title) and the Rotterdam tournament, extends his winning streak this year to 14-0. Federer, who earned his fifth title at Indian Wells past year, saved a set point in the second-set tiebreaker and advanced to face Filip Krajinovic yesterday.
Djokovic scrambled to win the second set on Sunday but the rust from the layoff was evident as he made 62 unforced errors overall.
Daniel, who is ranked 109th in the world, advanced to the third round, where he will face Gael Monfils of France, who outlasted American John Isner 6-7 (5-7), 7-6 (7-3), 7-5.
Borna Coric of Croatia upset 13th seed Roberto Bautista Agut 6-1, 6-3 and Spain's Pablo Carreno Busta defeated Daniil Medvedev 6-1, 7-5.
The win sets up a third-round showdown with Spaniard David Ferrer, who defeated Tennys Sandgren of the U.S. 6-2, 7-6 (7-3). "She's the best player I have ever played, and it was the biggest court I have ever played on".