Australia's top-ranked player Alex De Minaur, the world No.10 who is seeded ninth in this tournament, scored an impressive 6-2 6-2 win over Belgian veteran David Goffin in the California desert on Saturday (Sunday AEDT).
De Minaur's victory was the only joy for the Aussie contingent, with Adam Walton and Rinky Hijikata both losing in straight sets.
Canadian world No.28 Denis Shapovalov scored a comfortable 6-3 6-2 win over the 96th-ranked Walton.
Hijikata put up a strong effort in the first set against Brandon Nakashima, before the American pulled away in the second to win 7-5 6-1.
In the day's biggest shock, Serbian superstar Djokovic suffered an early exit at the hands of a lucky loser for a second consecutive year.
Djokovic fell to lucky loser Luca Nardi of Italy last year, and history repeated itself on Stadium One court a day after top-seeded German Alexander Zverev also went out.
The 24-time grand slam champion got off to a horrid start on Saturday, hitting 14 unforced errors and being broken twice in the opening set.
He regrouped to race out to a 3-0 lead in the second, levelling the contest with a mighty forehand winner and pumping his fist in front of the packed, sun-soaked crowd.
But van de Zandschulp ran away with the decider, breaking Djokovic for a fourth time with a perfectly executed lob for a 3-1 lead and sealing the stunning upset when Djokovic's shot went wide on match point. The final score was 6-2 3-6 6-1.
"I started really well and then of course Novak came back," said van de Zandschulp, who secured a spot in the tournament after the withdrawal of 47th-ranked Facundo Diaz Acosta.
"In the end I was happy to get my level back."
Van de Zandschulp was up a set and 3-0 on Nick Kyrgios in his first-round match before the Australian withdrew with wrist pain.
Djokovic, 37, retired from his Australian Open semi-final against Zverev with a hamstring injury, then lost in the Qatar Open first round last month.
He said the leg injury was behind him coming into the tournament, and he did not look hampered by it in his match on Saturday, where he was accompanied by coach Andy Murray.
"No excuses for a poor performance," Djokovic said.
"It doesn't feel great when you play this way on the court, but congratulations to my opponent. Just a bad day in the office."
The Serb's loss led a day of upsets that included Russian seventh seed Andrey Rublev losing 6-4 7-5 to Italy's Matteo Arnaldi, and 17th seed Felix Auger Aliassime falling to American Jenson Brooksby 6-4 6-2.
Earlier, Carlos Alcaraz began his bid for an Indian Wells three-peat with a 6-4 6-2 win over Quentin Halys.
Alcaraz is looking to join Djokovic and Roger Federer as the only players to have triumphed three successive times in "Tennis Paradise".
Alcaraz plays Shapovalov in the third round.
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