Sinner was pushed hard by the 19-year-old Brazilian, trailing 3-6 in the first-set tiebreak before rallying to close out the match 7-6 (8-6) 7-6 (7-4) in the Southern California desert on Tuesday (Wednesday AEDT).
"I am very happy winning this match," the Italian said.
"Joao is an incredible talent. He was serving really well. I was trying to be as aggressive as possible and that was the key to get through against the incredible talent."
Four-time major winner Sinner next meets the home favourite Learner Tien on Friday (AEDT) for a place in the last four.
"I feel he (Tien) is a very consistent player and I am very happy to face him again. He has improved a lot since the last time we met," Sinner said of his American opponent.
In other fourth-round action, Germany's Alexander Zverev saw off Frances Tiafoe 6-3 6-4, converting two of three break points and firing 14 aces to seal his ninth win over the 21st-seeded American.
He will next face France's Arthur Fils as he looks to reach his first Indian Wells semi-final.
Fils earlier produced a stunning 6-3 7-6 (11-9) win over Canadian ninth seed Felix Auger-Aliassime, saving five set points and rallying from 0-5 down in the second-set tiebreak to book a place in the quarter-finals for the second consecutive year.
Australia's sole remaining player in the men's draw, Rinky Hijikata, plays his fourth-round match on Thursday (AEDT).
Hijikata belied his world ranking of No.62 to beat the 10th seed Alexander Bublik in three sets on Tuesday (AEDT) and book his spot in the round of 16.
He next takes on English left-hander Cameron Norrie, who beat sixth-seeded Australian Alex de Minaur in straight sets in the third round.
In the women's draw, Talia Gibson will fly the Australian flag on Friday (AEDT) when she takes on 14th-seeded Czech Linda Noskova in the quarter-finals.
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