Though most of the crowd at Indian Wells came to see the former World No. 1 in his comeback following right elbow surgery, it was the 25-year-old Daniel who stole the show with a scrappy 7-6 (3), 4-6, 6-1 victory.
The Swiss tennis legend needed an hour to close out his second-round victory 6-3, 7-6 (8-6).
Federer and Delbonis resumed their match from Saturday which was called off by rain with Federer up by one set. After another 90-minute delay organizers suspended play for the night.
Federer and Djokovic both came into the tournament seeking to become the first six-time victor of the event.More news: Credit Agricole SA Sells 499645 Shares of Occidental Petroleum Co. (OXY)
He added, "Very weird".
The Serbian was making his first comeback after undergoing elbow surgery earlier this year.
Djokovic bounced back in the second, but Daniel took advantage of his opponent's poor form to win the third. "And even though you don't have pain, you are still thinking about it, because it has been something that I have been feeling and dragging for over two years", Djokovic said.More news: Aston Villa boss Bruce: Terry our biggest name - we need him now
"To me, his loss is not that surprising", Federer said. "So talking about faster, I just think there is more bounce to it, especially if you play someone who has a lot of spin like he has and kicks the ball around a lot".
"It is still early stages for Novak coming back and the first one after surgery".
Among the other losers on Sunday were Germany's Alexander Zverev, who lost to Portugal's Joao Sousa 7-5, 5-7, 6-4, and American John Isner, who was defeated by France's Gael Monfils 6-7 (5), 7-6 (3), 7-5 in a gripping match, in which both players struck a total of 23 aces. Let's just say Jeremy Chardy is going to get his full attention over the next couple of days. The No. 3, 4, 6, 9, 11, 12, 13, 14 and 15 seeds are all gone.
In other men's matches, David Ferrer of Spain defeated Tennys Sandgren of the United States 6-2, 7-6. World number three Marin Cilic also won Sunday, defeating Hungary's Marton Fucsovics in straight sets, 7-5, 6-3.More news: Bill on chit funds sector introduced in Lok Sabha