In action for the first time since the Australian Open as he continued to recover from an elbow injury, Djokovic - the 10th seed - went down to Daniel 7-6 (7-3) 4-6 6-1.
Both Djokovic and Edmund were making their first appearances since the Australian Open.
As his form began to dip at the end of 2016, Djokovic admitted that he had been affected by off-court issues that he hasn't elaborated on. What was mystifying was that he looked strong and precise in the early phases of his three-set loss to Japanese qualifier Taro Daniel in the second round. Less than 24 hours later, he was back on the court, where he finished off Federico Delbonis 6-3, 7-6 (6).
A lot was expected of Djokovic, but the Serb was rusty and made 61 unforced errors in the match against Daniel that lasted two hours and 30 minutes.
"I just completely lost rhythm, everything", said Djokovic.
Roger Federer didn't rule out the clay season, at least not yet, he said yesterday at Indian Wells. "When you go from night to day, (normally you are) playing a different opponent, so naturally, it's all a change". Should he fall before the semi-finals, Rafael Nadal will return to top spot because he is only dropping 90 points from his fourth-round result in Indian Wells last year.More news: Newcastle boss Rafa Benitez has full belief in his team
Meanwhile, Kei Nishikori pulled out ahead of his opening match due to illness.
Federer improved to 65-5 since returning from a left knee injury last year with his third-round victory in a rare day match.
The world No. 25 had been scheduled to face Argentina's Leonardo Mayer in a second-round match. Chardy has played eight sets already this tournament and has been very shaky with his second serve recently. If he can't clean up a shot that was once his most reliable, nothing is a given right now. "It was a good day".
"For me it felt like the first match I ever played on the Tour", said Djokovic.
Federer's match was not the only one postponed by a persistent rain Saturday evening. Federer was then enduring some very poor form and proved a rather different proposition for Delbonis in the Californian desert.
Federer barely raised a sweat as he advanced on Monday, the evergreen 36-year-old blitzing Filip Krajinovic 6-2, 6-1.