World No 1 Roger Federer was held up by rain as he began the defence of his BNP Paribas Open title at Indian Wells on Saturday.
Federer will maintain his No. 1 ranking if he advances to the semifinals at Indian Wells.
Returning on Monday morning (AEDT), Federer survived a set second scare for a 6-3 7-6 (6) win.
In a rain-hampered match, Federer won the first set on the weekend, before the wet weather forced play to be delayed overnight.
"I didn't come here to lose in the first round two and two", Federer told reporters.
The match was suspended due to rain at 2230 local time poised with the second set tied at 2-2, and no further play was possible. After another 90-minute delay organizers suspended play for the night.More news: NIT 2018: Penn State will play Temple as No. 4 seed
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In the tiebreaker, Federer took a 5-2 lead but Delbonis battled back to win a long rally and tie it 5-5.
Grigor Dimitrov will not be in round three after the third seed fell to Spanish veteran Fernando Verdasco 7-6 (7/4) 4-6 6-3.
It was the earliest loss for Djokovic at Indian Wells since a first-round exit in 2006.
Daniel, who is ranked 109th in the world, advanced to the third round where he will face Gael Monfils of France who outlasted American John Isner 6-7 (5/7), 7-6 (7/3), 7-5. With Delbonis claiming victory in the only other match the pair have played - a 7-6 (7) 7-6 (4) win in Hamburg in 2013 - there was cause for concern.