Nadal is now out with a recurrence of his hip injury, Djokovic is struggling after elbow problems and Murray is recovering from major surgery in January.
Djokovic was makings his first appearance since being stunned by Hyeon Chung at the Australian Open.
Rain barred Federer from completing the first match of his title defence at the season's opening ATP Masters 1000 tournament on Saturday. He was trailing Pablo Cuevas 6-3 4-6 2-4. Daniel plays next Argentinean tennis player Leonardo Mayer.
'You can't really look ahead to semi-finals, finals and speculate about who you could play, ' Federer said.
Delbonis, who is ranked 67th in the world, is no stranger to upsets in Indian Wells.
"I didn't come here to lose in the first round two and two", he said.
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.
But the decision backfired as he peppered the court with 61 unforced errors and totally faded away in the third set in the second round clash that lasted 2 hours 30 minutes.
Other seeded players who lost were ninth-seeded Lucas Pouille, who fell 6-4, 6-4 to Yuki Bhambri; 14th-seeded Diego Schwartzman, 7-5, 6-4 to Marcos Baghdatis; 21st-seeded Kyle Edmund, 6-4, 6-4 to Dudi Sela; and number 24 seed Giles Muller, 6-3, 7-5 to Pierre-Hugues Herbert.
He will face 25th-seed Filip Krajinovic in the third round.
A five-time victor at Indian Wells, Federer needed less than an hour to crush Krajinovic.
Frenchman Gael Monfils survived a match point before beating big-serving American John Isner 6-7 (5) 7-6 (3) 7-5 in a contest that had only one break. "I have been sick for over a week and tried everything I could to get better". Fifth seed Karolina Pliskova too needed three sets to reach the fourth round but the French Open titlist Jelena Ostapenko bowed out.