After the world number one stormed to the first set over the weekend, rain interrupted play, forcing a delay overnight.
No. 30 Pablo Cuevas beat up-and-coming Canadian Denis Shapovalov 7-6 (4), 6-3.
Federer is making his 17th appearance in the California desert and is assured of remaining world No 1 if he makes it to the semi-finals. The 12-time Grand Slam champion was playing his first competitive match since recovery from a wrist injury that hampered his Australian Open campaign in January 2018.
Federer won the Indian Wells championship for a fifth time previous year, adding to his crowns in the Southern California desert in 2004, 2005, 2006 and 2012.
Federer wasted a game point at 5-5 with another forehand mistake and he got broken when his backhand found the net three points later to send Canas 6-5 in front.
After losing to Hyeon Chung in the fourth round of the Australian Open, Djokovic took some time to get himself healthy.
On his return from right elbow surgery, Djokovic looked a pale shadow of his former self as he went down 7-6 (3) 4-6 6-1 to make a quick exit from a tournament he has won five times.
Djokovic said it felt like the "first match I ever played on the tour". "I'd like to congratulate my opponent for fighting and showing great, great spirit on the court", said Djokovic.
"I just completely lost rhythm, everything", a candid Djokovic told press.
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"Just struggled also a bit with the health the last couple of weeks".
Djokovic scrambled to win the second set on Sunday but the rust from the layoff was evident as he made 62 unforced errors compared to 29 for Daniel.
"It feels insane. I mean, I'm still in shock", Anisimova said.
Novak Djokovic during his second round match against Taro Daniel.
"Tennis was always my life since I'm a baby", said Verdasco. Honestly making - I think, if I'm not wrong, in two games two double faults on each one, and giving him the possibility to go 3-0 in the score with two breaks. When you do come back from injury or when you haven't played in a long time, it just takes extra effort.
"Look, still such early stages for Novak coming back and the first one after surgery". Because if I change and I start to put, like, kind of like first, second serves in to try to play with first serve, but then also doesn't hurting him so much, maybe, you know, he was returning so much, like, on top of the line, if he connect two or three good returns, it was going to be tough.
Daniel, a 25-year-old ranked 109th in the world, hadn't won a main-draw ATP World Tour event this year before Sunday.
Meanwhile, two-time champion Victoria Azarenka's comeback was short-lived as she fell 1-6, 5-7 to the 2017 US Open champion Sloane Stephens in Round 2.