Thiem denied Federer the chance to claim his record-breaking sixth title at Indian Wells after his 3-6, 6-3, 7-5 victory.
The 18-year-old was ranked No.60 coming into the tournament but will now rise to 24th following his maiden WTA title.
Nadal will be gunning for his fourth Indian Wells title while Federer is seeking to break out of a tie with Djokovic with a record sixth.
Nadal also confirmed he won't compete at next week's Miami Masters, targeting a return to competition at Monte Carlo April 14-21.
After toppling Elina Svitolina in three sets, Canada's Bianca Andreescu will face Wimbledon champion Angelique Kerber for the title.
Earlier this week, Prajnesh Gunneswaran made heads turn at the Indian Wells Masters thanks to significant victories over Benoit Paire and Nikoloz Bas
Osaka lost to Belinda Bencic 6-3, 6-1 in just over an hour in the fourth round of the first title defense of her career.
World number two Nadal overpowered Serbian qualifier Filip Krajinovic 6-3, 6-4 to book his quarter-final berth in one hour and 26 minutes.
Kohlschreiber notched his first ever victory over a number one-ranked player, ending Djokovic's bid for a sixth Indian Wells crown.
Giron, 25, looked set to claim the biggest win of a career that has been hindered by two hip operations when he took a 4-1 lead in the third set.
Rohan Bopanna and his partner Denis Shapovalov were knocked out by Novak Djokovic and Fabio Fognini in the second round.
Exactly 365 days ago, Prajnesh Gunneswaran had landed in the tennis outpost of Chandigarh to take part in a low-level Futures event.