Poland's Swiatek, a six-time Grand Slam champion ranked second in the world, coughed up eight double faults in a rocky performance.
The experienced Svitolina made the most of the early chances she was given and held her nerve in a tense third set to reach the Indian Wells semi-finals for the second time, and the first since 2019.
She gained the lone break of the final frame as she won the last three games to take the match.
"I wouldn't say it was the perfect match, but I could stay in the match and fight and find a way after losing second set," Svitolina said.
"There is no champion who is waiting for the mistakes, and you have to really try to set up yourself in a good position to attack," she added. "I was trying to really open up the court and try to take the advantage, because Iga is such an aggressive player, and she moves really well. So if you don't take the opportunity, she's going to take it."
Svitolina closed it out in style, giving herself a match point with an ace and nailing a forehand volley to reach the Indian Wells semi-finals for the first time since 2019.
"You make me feel a bit old with that stat," quipped the 31-year-old Svitolina, who returned to the top 10 in the world rankings in February for the first time since 2021 and the first time since becoming a mother.
It was just her second career win over Swiatek in six meetings and her first since 2023. But the victory continued a rich run of form in 2026 that has seen Svitolina capture the title in Auckland and finish runner up in Dubai last month.
For six-time Grand Slam champion Swiatek it was another disappointing quarter-final exit this year after she fell at the same stage in the Australian Open and in Doha.
She closed it out in style, breaking Swiatek for a 5-4 lead then giving herself a match point with an ace and nailing a forehand volley.
Svitolina, winner of the title in Auckland to start her year and runner-up to Jessica Pegula in the WTA 1000 in Dubai last month, will face Elena Rybakina, the 2023 Indian Wells champion, who booked a return to the semi-finals with a 6-1, 7-6 (4) win over Pegula, who fell to the Kazakh in the semi-finals in Melbourne.
Rybakina recouped a break that had her trailing 4-1 in the second set and put on a serving clinic in the tiebreaker to end Dubai champion Pegula's eight-match winning streak.
Sabalenka downs teen sensation Mboko
World number one Aryna Sabalenka kept her bid for a first Indian Wells title on track, holding off Canadian teen Victoria Mboko 7-6 (0), 6-4 to reach the semi-finals on Thursday.
Sabalenka had beaten Mboko in the fourth round of the Australian Open in January in a match the 19-year-old called "an eye-opener."
This time around, Mboko, ranked 10th in the world, went toe-to-toe with the big-hitting Belarusian in the opening set before Sabalenka ran away with it in the tiebreaker.
Mboko regrouped admirably to open the second set with a confident service hold.
But Sabalenka finally cracked Mboko's serve on her seventh opportunity, conjuring the first break of the match for a 3-2 lead and fighting off a pair of break points in the eighth game to bring it home.
"It was a tough battle today," Sabalenka said. "Super happy with the performance. Happy the level I played on those key moments in each set."
Sabalenka, who came up empty in trips to the final of the ATP and WTA Masters 1000 in California in 2023 and 2025, next faces either 14th-ranked Czech Linda Noskova, who ended the dream run of Australian qualifier Talia Gibson, 6-2, 4-6, 6-2.
Sabalenka said she'd seen a "big improvement" in Mboko's game since they met in Melbourne.
"I think she was serving much better than she did in that match in Australia," Sabalenka said. "Definitely a bit more confident and was playing more brave."
Mboko agreed but said there was room for more improvement.
"It's never easy to play the world number one," she said. "I had a lot of chances in the first set ... but she was playing really well, especially on pressure points. I've got to give credit to her there.
"I feel like I was maybe one or two points away from changing how the first set would have went ... that's something I could work on for the next time."
Noskova looked headed for a comfortable victory over Gibson, whose fourth-round win over seventh-ranked Jasmine Paolini was her first over a top-10 foe.
The 112th-ranked Australian surged back after breaking Noskova to open the second set. She held on to the advantage to force the third, only for the Czech to seize control again.
