"When you go from night to day [in consecutive days, you're usually] playing a different opponent", said Federer, who couldn't remember the last time he had played a match that was interrupted overnight.
Less than 24 hours later, he was back on the court, where he finished off Federico Delbonis 6-3, 7-6 (6).
The match was tied 2-2 in the second set when it was halted Saturday.
The Spaniard once ranked No. 7 in the world is now ranked No. 39 said: "Well, I think that the match kind of, like, went up-and-downs a little bit, at least the two first sets with a break that he made me at the beginning". After another 90-minute delay organisers suspended play for the night.
Federer is making his 17th appearance in the California desert and is assured of remaining world number one if he makes it to the semi-finals in Indian Wells.
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. Bhambri will face either 18th seed Sam Querrey or Mischa Zverev next.
Djokovic, who won the Indian Wells event in 2008, 2011, 2014, 2015 and 2016, was knocked out early for the second year in a row.
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.More news: Kawhi Leonard could return as early as Tuesday
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"It feels insane; I mean, I'm still in shock", said Anisimova, whose parents are Russian but who represents the United States, where she was born and raised. Daniel defeated Djokovic 7-6 (7/3), 4-6, 6-1 in the hard-fought victory.
Argentina's del Potro, who is fresh off winning the Mexican Open title in Acapulco, hammered five aces and broke de Minaur's serve five times.
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 previous year and then undergone surgery following a fourth-round loss at the Australian Open.
Discussing his display, Djokovic said: "Nerves were there".
Novak Djokovic during his second round match against Taro Daniel.
Federer said he understands well how even a champion like Djokovic could be struggling to find his game so soon after having surgery. "But at the same time, I just didn't feel good at all", he added. 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. "And I just have to work really hard and keep that motivation high to be able to win matches". He's only going to get better from here.
Daniel, a 25-year-old ranked 109th in the world, hadn't won a main-draw ATP World Tour event this year before Sunday.
In another upset, No. 16 Fabio Fognini lost to Jeremy Chardy 4-6, 7-6 (2), 6-4.