The home hope was cheered on by the California crowd as she reached her first WTA 1000 quarter-final.
Meanwhile, American third seed Coco Gauff claimed an emphatic 6-0 6-2 win over Belgium’s Elise Mertens.
Playing on her 20th birthday, the 2023 US Open champion wrapped up a first-set bagel in 25 minutes.
Mertens finally got on the board with a break and held serve to level the second set at 2-2, but Gauff regained control and won four games in a row to reach the last eight at Indian Wells for a second straight year.
“I feel really good. That’s my best match of the tournament so far and I’m obviously happy to get the win on my birthday,” Gauff told Sky Sports.
Both Gauff and Navarro are bidding to become the first American woman to win at Indian Wells since Serena Williams in 2001.
Gauff will play either Russian 11th seed Daria Kasatkina or China’s Yuan Yue in the semi-finals, while Navarro will face Greek ninth seed Maria Sakkari or France’s Diane Parry.
Claiming the first break of the match in the eighth game, Navarro saved a break point before serving out the opening set, but Sabalenka fought back to win the second.
After exchanging breaks early in the decider, Navarro struck again for a 3-1 lead as Sabalenka’s serve faltered and, after saving the first match point, the two-time major winner missed the second to hand Navarro the biggest win of her career.
The victory continues a strong season for the 22-year-old, who claimed her first WTA Tour title in January at the Hobart International.
“I’m feeling really good, it’s never easy coming out and playing an opponent like that – so experienced and just so talented,” Navarro said.
“She made it really tough on me today, but I was glad I was able to play some good tennis in the big moments.”