Daniel, speaking on the biggest win of his career, said, "It's kind of hard to describe.I can't believe I beat someone like that on the center court like this; it's insane".
Djokovic took six months off after Wimbledon previous year and returned in January's Australian Open where he lost in the fourth round.
But Djokovic fell at the first hurdle with a shock loss to Japanese qualifier Taro Daniel, who sent the out-of-sorts Serb tumbling with a hard-fought 7-6 (7-3), 4-6, 6-1 victory.
Following his exit in Melbourne, it was the 12-time Grand Slam winner's first appearance at the 2018 BNP Paribas Open.
It was the former world No.1's first match since returning from an injury, which forced him to undergo a surgery earlier in February.
"To me, it's not that surprising", the defending champion said in California. 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. "I mean, I just completely lost rhythm, everything".
Federer, who defeated Federico Delbonis in the second round, will next face Jeremy Chardy after the world No 100 overcame countryman Adrian Mannarino, world No 23, 7-5 4-6 6-1. "When you go away from the game for over a two-month period, it starts feeling a little bit that way", the Express quoted Federer as saying. "He's only going to get better from here", concluded the world number one. "She's the best player I have ever played, and it was the biggest court I have ever played on".
"I was attacking when I had my chances and controlling most of the times the points", said Cilic.
This was even as Novak Djokovic and Kei Nishikori have both been eliminated. So it was definitely nerve-wracking kind of, but I was enjoying it so much out there and I was playing my best. That comes over playing a good schedule with the right amount of practice, vacation, matches, everything.