Swiatek came under pressure early in the opening set but some clean ball striking helped her hold for a 3-2 lead after two tight service games. She raised her level further to break Raducanu in the next game before pulling away.
Having wrapped up the first set when Raducanu sent a shot long from the baseline, Swiatek grabbed an early break in the second to heap the pressure on the Briton, whose unforced errors began to mount.
Swiatek, bidding to become only the second female player to successfully defend the Indian Wells title after Martina Navratilova in 1990-91, raced to a 5-1 lead playing flawless tennis and running her opponent ragged.
The US Open champion closed out the win when Raducanu struck the net on serve in a tame end to her fine run in the Southern California desert.
After taking the first set, the sixth-seeded American began to struggle with her forehand in the second and an opportunistic Peterson began to apply pressure by coming into the net.
But after suffering an early break in the decider, Gauff stepped up her defence, fending off three break points at 4-4 and breaking Peterson for a fourth time on match point to book her spot in the last eight.
Gauff, who turned 19 on Monday, was serenaded with a rendition of "Happy Birthday" after the match by the partisan crowd in the Southern California desert.
"Today, it was just a mental thing, staying in the match," Gauff said.
"I wasn't playing my best in some moments and wasn't serving as well as I'd like to, but I think my mentality kept me in today."
Next up for Gauff is a meeting with Belarusian second seed Aryna Sabalenka, who survived a second-set scare to beat 16th seed Barbora Krejcikova 6-3 2-6 6-4.
Sabalenka sent down 11 aces in the match to secure victory and get revenge on the Czech, who beat her at last month's Dubai Tennis Championships.
Elsewhere, seventh seed Maria Sakkari outlasted big-serving Czech Karolina Pliskova 6-4 5-7 6-3 in a two-hour and 45-minute marathon to reach the quarters.
With the win the Greek keeps alive her hopes of capturing a first Indian Wells crown after making the final last year.
Sakkari will next face Czech 15th seed Petra Kvitova for a semi-final spot, after the two-time Wimbledon champion saved four match points en route to a 6-2 3-6 7-6(11) win over third-seeded American Jessica Pegula.
"I play for these emotions," Kvitova said after the epic encounter.
"The match was up and down, a disaster at times. I knew that Jessica will not miss, but I still had to go for it. I think this might be one of the best matches I played..."
Cirstea bagged her first top-five win since 2017 in Beijing as the she battled past fifth seed Caroline Garcia 6-4 4-6 7-5.
Wimbledon champion Elena Rybakina beat Varvara Gracheva 6-3 6-0 and will next take on Karolina Muchova, who overcame Marketa Vondrousova 6-4 6-7(2) 6-4.
