Eala, 20, was leading 6-2, 2-0 when Gauff threw in the towel, having received treatment on her left arm during an injury timeout late in the final set.
A trainer worked on Gauff's shoulder and arm and after she was broken in the final game of the opening set, returned to wrap her forearm.
It was to no avail, and Gauff went to the net and told Eala she was calling it a day after dropping her serve in the second game of the second set.
"I really didn't want to win this way," Eala said.
"But this is still a really big moment for me to be able to play on Stadium One of Indian Wells and against such a great competitor," she added, wishing Gauff a speedy recovery.
Eala will face Czech Linda Noskova for a place in the quarter-finals.
Japan's Osaka, seeded 16th, pounced for a 6-1, 3-6, 6-1 victory over Camila Osorio to avenge a demoralizing first-round loss to the Colombian here last year.
Sabalenka is chasing a first title in the prestigious ATP and WTA Masters 1000 event after twice coming up empty in the final.
Osaka won her first title in Indian Wells in 2018, going on to win the US Open that year in a run that included a victory over Sabalenka.
That's the only meeting to date between the two - who are now both four-time Grand Slam champions
There were a few blips, notably a double fault on break point as she served for the opening set. Sabalenka responded by breaking Cristian to pocket the set and was satisfied with an overpowering performance.
"I knew that she was not going to give up easily," she said. "That's why I was super-focused, especially on my serve. I didn't want to give her much opportunity so super-happy with the serving, with the game and of course with the win."
Sixth-seeded American Amanda Anisimova faces another former Grand Slam champion in Britain's Emma Raducanu, who last month reached her first WTA final since her shock run to the 2021 US Open title.
Fourth-seeded Coco Gauff headlines the night session, taking on rising Philippines star Alexandra Eala - who gets a quick chance for revenge after falling 6-0, 6-2 to the American in the Dubai quarter-finals last month.
"I'm excited," Eala said. "It was a tough match for me last time. I think she played really well. So all I can do is take the learnings that I have from our last match and try to implement that in our next one."
Gauff, coming off an "awkward" 6-3, 7-6 (5) win over qualifier Kamilla Rakhimova, can expect plenty of crowd support. But so can Eala, who is drawing her usual contingent of loyal Filipino fans in the California desert.
"It means the world to have this community behind me in such a prestigious tournament," Eala said after enthusiastic fans backed her through a chilly, late-night win over Dayana Yastremska. "It really added to the feelings and the emotions after the match."