Marin Cilic, the 2014 U.S. Open champion who lost to Federer in the final of this year's Australian Open, eased to a 7-5, 6-3 victory over Marton Fucsovics.
"It's been a long time since I have been interrupted at night and have to come back the next day", he said.
Federer staved off a set point in the tiebreak to beat Delbonis 6-3 7-6 (6). His title defence got off to a soggy start Saturday night when play was suspended because of rain showers with Federer up a set and tied 2-2 in the second.
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Djokovic, 30, was making his first appearance since an injury ended his Australian Open campaign in January.
"In Rotterdam I played five matches in a row", he said.
On his return from right elbow surgery, Djokovic looked a pale shadow of his former self as he went down 7-6 (3), 4-6, 6-1 to make a quick exit from a tournament he has won five times.
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"I was feeling like he was not loving my slice and I was also mixing in dropshots", said Federer who extended his flawless record this season to 14-0. Djokovic scrambled to win the second set on Sunday but the rust from the layoff was evident as he made 62 unforced errors overall.
The only thing rarer than a raindrop in the Southern California desert might be a Roger Federer early-round loss, and thankfully for fans, the weekend brought only one of those anomalies. "When you go away from the game for a two-month period, it starts feeling a little bit that way".
"At the same time, I enjoy playing the guy, just because it's one of the ultimate challenges to play Novak, Andy, Rafa, Stan, you name it, all these guys".
Spanish 11th seed Pablo Carreno Busta defeated Daniil Medvedev 6-1 7-5 but 13th-seeded Roberto Bautista Agut was dismantled 6-1 6-3 by 21-year-old Croatian Borna Coric.
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Plus, there's the matter of Wade Phillips, who was Talib's defensive coordinator in Denver, now in that same position in Los Angeles.
Caroline Garcia also progressed in straight sets against Daria Gavrilova.