Swiatek edged Collins in an epic at the Australian Open and the familiar foes appeared primed for another blockbuster when they were on serve with the Pole leading 4-3 in the first set.
But Swiatek raised her level from there, breaking to love for 5-3 and winning the final nine games to advance at the tournament she won in 2022.
"I started to make a few less mistakes, which gave Danielle a chance to make a few more," Swiatek said.
"It's a small difference but at the end, I was ready to play well in those important moments, on break points and stuff like that. I'm happy I kept my focus and stayed with my game, no matter what Danielle was doing on the other side of the net."
Collins in January said she would retire at the end of the season so this is expected to be the 30-year-old's final appearance at Indian Wells.
The American beat Swiatek decisively to reach the Australian Open final in 2022 and achieved a career high ranking of world number seven.
Kerber scored her biggest win in three years with an impressive 5-7, 6-3, 6-3 victory over hard-hitting Latvian Ostapenko.
The German, who returned to the tour in January after 18 months on maternity leave, fired an unreturnable serve on match point to seal her first win over a top 10 opponent since November 2021.
"This question I heard a lot, why I'm back and what gives me the motivation," the three-times Grand Slam champion said.
"For me, the biggest motivation is the love for the sport. I love to compete, being out there today as well, having this crowd, having the emotions, this gives me everything.
"Now, having my daughter on my side, it's even more inspiring for me to have her, and there's something bigger than tennis as well."
