Djokovic is a 12-time Grand Slam champion and former World No 1 but was only seeded 10th here, having taken six months off after Wimbledon a year ago and then undergone surgery following a fourth-round loss at the Australian Open.
INDIAN WELLS-Rain suspended Roger Federer's opening-round match in the second set last night. Daniel sent an out-of-sorts Djokovic tumbling with a hard-fought 7-6, 4-6, 6-1 victory.
"Nerves were there. I made so many unforced errors".
Federer wrapped up a 6-3, 7-6 (6) triumph over Delbonis with a flourish soaring for an artistic high-backhand volley to charge into the BNP Paribas Open third round.
Unfazed, Federer reeled off three straight points to close in one hour, 41 minutes.
"It felt like first match I ever played on the tour, " Djokovic said.
Djokovic's performance in the final set against the world's 109th-ranked player on centre court raised some eyebrows. They previously clashed in the final of the Buenos Aires Challenger previous year, with Daniel rallying for a three-set win.
Roger Federer is gunning to retain his world No 1 title at Indian Wells this week.
"It feels insane. I mean, I'm still in shock, " Anisimova said.
"Very weird. I completely lost rhythm", admitted the Serb.
Yuki Bhambri of India pulled off a surprise when he toppled ninth-seeded Frenchman Lucas Pouille 6-4 6-4.
Jack Sock, David Ferrer, Marin Cilic were also winners along with Gael Monfils who edged John Isner and Milos Raonic who ended the run of Canadian countryman Felix Auger-Aliassime 6-4, 6-4. "The surface doesn't react so much", he said.
"But, you know, after an opponent like this, to come back from two breaks down, actually, for me it was nearly impossible. 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".
By virtue of the win, Federer moved on to the third round where he will face No. 25 Filip Krajinovic for a spot in the round of 16.
Amid a conversation with the umpire and Delbonis on court, Federer could be heard telling his Argentine opponent: "I can start but if you don't wanna start we don't have to".