Meanwhile, Japanese qualifier Taro Daniel sent five-time tournament champion Novak Djokovic tumbling out with a hard-fought 7-6 (7/3), 4-6, 6-1 victory.
No wonder the injury hit Djokovic uttered to reporters afterward: "For me it felt like (the) first match I ever played on the tour". Appearing in his second tournament in the last nine months, the Serbian lacked pace, was slow and without confidence during Sunday's encounter, reports Efe.
The top seed fended off a set point in the tiebreak to beat Delbonis 6-3, 7-6 (6).
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. Find us on Facebook too!
"Getting through qualifying made me a bit more confident, which gave me the belief.to get through the tougher moments, even against someone like (Djokovic)", he said.
Djokovic took six months off after Wimbledon past year and returned in January's Australian Open where he lost in the fourth round. "Very weird. I mean, I just completely lost rhythm, everything".
Thiem has already won a tour-leading 17 matches this season, but he had to work hard to beat 19-year-old Tsitsipas, who reached the quarter-finals in Dubai last week and is ranked 71st in the world.
Djokovic bounced back in the second, but Daniel took advantage of his opponent's poor form to win the third.
Federer returned to stadium court on Sunday afternoon and needed an hour to close out his second-round victory 6-3, 7-6 (8/6).
Storm clouds rolled in just before the start of their match on Saturday and after a short delay to start the first set they managed to play until the heavy rains came in the second.
"I have been sick for over a week and tried everything I could to get better".
It was the earliest loss for Djokovic at Indian Wells since a first-round exit in 2006.
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.
Spanish veterans David Ferrer and Feliciano Lopez recorded routine straight-sets wins over Tennys Sandgren and Ernesto Escobedo respectively while Philipp Kohlschreiber outlasted Tim Smyczek.