The defeat was just the fifth time in the past decade former world number one Djokovic has lost against a player outside the top 100 players in the world.
On Sunday, he finished off his two-day 6-3, 7-6 (8-6) victory over Federico Delbonis to set up a third-round clash with 25th seed Filip Krajinovic yesterday (this morning, Singapore time).
In some of the other matches of the day, second seed and Australian Open runner-up Marin Cilic edged a tight first set and then raced through the second for a 7-5, 6-3 win over Marton Fucsovics.
Rain barred Federer from completing the first match of his title defence at the season's opening ATP Masters 1000 tournament on Saturday. After another 90-minute delay organisers suspended play for the night. But 16-year-old Amanda Anisimova, the reigning junior US Open champion, put paid to her hopes as she sent the two-time Wimbledon victor packing with a stunning 6-2, 6-4 win in the third round.
Bhambri will face either 18th seed Sam Querrey or Mischa Zverev next. "Very weird", Djokovic said.
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"Just struggled also a bit with the health the last couple of weeks".
Federer stressed it was always going to be hard for the six-time Australian victor to impress on his return from injury, which is why the 36-year-old was not surprised following Djokovic's struggle in Indian Wells.
Djokovic was making his first appearance since being stunned by Hyeon Chung at the Australian Open.
However, Daniel bounced back as he won the third set comfortably to clinch the match.
Federer was at his trademark best, fluid and graceful as the Swiss star broke in the fourth game for a 3-1 lead and never looked back. "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".
Delbonis, who is ranked 67th in the world, is no stranger to upsets in Indian Wells. He's only going to get better from here.