Badosa, who made this year's French Open quarter-finals, squandered two match points at 5-2 in the second set against three-time grand slam champion Kerber before steadying to secure her fifth final-four appearance of the season on Friday (AEDT).
In the semi-finals, Badosa will face Tunisian Ons Jabeur, the No.12 seed, who got past Anna Kontaveit in straight sets, confirming her historic rise into the top 10 of the rankings, as the first-ever Arab player to achieve the singles feat on either the WTA or ATP Tour.
Former world No.1 and No.10 seed Kerber bowed out at Indian Wells, with Badosa triumphing 6-4 7-5 in 86 minutes.
In her Indian Wells debut, No.21 seed Badosa responded strongly after fluffing two match points to become the first Spanish woman to make the event's semi-finals in 18 years.
"It sounds amazing," Badosa said during her on-court interview. "The second set was very mental. I wanted this match so badly. I got super nervous.
"For one second I thought who was on the other side of the net and I got more nervous against a three-time grand slam champion. It means a lot to me. It's amazing."
In the first set, Badosa broke Kerber at 4-4 before serving out the opening set where she was excellent on her first serve, staving off the German's only two break points.
The Spaniard raced to a 5-2 lead in the second set and had two match points on Kerber's serve. The experienced Kerber responded by holding serve and then breaking back, before levelling at 5-5.
But Badosa showed her mettle by winning the final two games, breaking Kerber for victory as she upped her level.
Jabeur defeated Estonian Kontaveit, the No.18 seed, 7-5 6-3 to move into the top 10 for the first time in her career.
The Tunisian will become the first Arab player to make the top 10 when the updated WTA rankings are made official on Monday, but she also qualified for the biggest semi-final of her career to date.
"It feels amazing," Jabeur said. "We've been working hard since years. When I spoke at the end of last season, I said I wanted to be in the top 10. People doubted us as a team, we proved them wrong.
"Being a top 10 means a lot but we're not going to stop here. We're going to go further hopefully."
Jabeur, who made this year's Wimbledon quarter-finals, triumphed in 86 minutes, although she did not have it all her way, in a match full of momentum swings.
The 27-year-old Jabeur had been a double break up at 4-1 in the first set before Kontaveit hit back to level at 5-5, only for her to break back immediately and serve out the set.
Jabeur broke Kontaveit to love at 3-3, rattling off the final three games, including two breaks, to secure victory and keep alive her hopes of making the WTA Finals.