"I didn't serve too good today but overall I'm pleased".
"I was feeling like he was not loving my slice and I was also mixing in drop shots", said Federer who extended his ideal record this season to 14-0.
After handing back an early break to allow Krajinovic to draw level at two-all, Federer moved into cruise control.
"I can't believe I beat someone like (Djokovic) on center court like this, it's pretty insane", Daniel said.
He said playing matches three days in a row doesn't faze him.
"I was grateful to be out on the court after surgery that quickly but at the same time just didn't feel good at all", he added.
If God played tennis he would be Roger Federer.
"At the Masters 1000s, when the format was different, it was the best-of-five-set finals in the finals".
With his triumph on Monday, Federer, victor of the 2018 Australian Open (20th Grand Slam title) and the Rotterdam tournament, extends his winning streak this year to 14-0.
Japan's Kei Nishikori withdrew through illness before playing his opening match of the tournament. It was the fifth time in the last decade that a player ranked outside the top-100 has defeated Djokovic.
In other matches, fifth-seeded Dominic Thiem had to retire with an ankle injury while trailing Pablo Cuevas 6-3 4-6 2-4.
Israeli Dudi Sela beat British 21st seed Edmund 6-4 6-4, while Luxemburg's 24th seed Giles Muller was upset by Frenchman Pierre-Hugues Herbert 6-3 7-5.
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 (7-3), 4-6, 6-1 victory.
Seventh seed Kevin Anderson took down Nicolas Kicker 7-6 (1) 7-6 (3) and South Korea's Chung Hyeon beat Tomas Berdych 6-4 6-4.