The Polish four-time Grand Slam winner had not dropped a set before Sunday's match but was unable to hold off the confident 20th seed’s charge.
She will see Belarusian Aryna Sabalenka replace her as world number one when the standings are updated after the tournament, after holding her place at the top since April 2022.
"When you lose it, there are some sad emotions," said Swiatek. "This season was really tough and intense. It's not easy to cope with all of this stuff."
Ostapenko fired off a crisp forehand winner to break her opponent's serve on match point, pumping her fist as she extended her career head-to-head record against Swiatek to 4-0.
The 2017 Roland Garros champion next faces American sixth seed Coco Gauff, who beat wildcard Caroline Wozniacki in three sets earlier in the day.
"I always expect a tough battle against Iga," Ostapenko said. "I knew I had to play my game. I have to be aggressive because that's what she doesn't really like and I was just fighting until the very last point."
Swiatek got off on the wrong foot, helping Ostapenko to a break in the first game with a double fault and a pair of forehand errors.
She broke back immediately, though, and converted on another break-point chance with a fine forehand winner in the sixth game before taking the first set.
But things began to fall apart for Swiatek in the second set.
She sent a forehand out to hand Ostapenko a break in the second game and was unable to convert a break point in the ninth game before Ostapenko tied the match at 1-1.
Swiatek looked demoralised in the third set while Ostapenko upped her level further, taking full control to cruise through the first five games and adding only two more unforced errors to her count en route to sealing victory.
The win extends Ostapenko's best run at the hardcourt major as she had failed to get past the third round in six previous main draw appearances.
"I had nothing to lose today. I knew it was going to be a tough match," she told reporters.
"Even the first set I couldn't find my game that way, but I was fighting and trying to find my game and be aggressive."
Swiatek was surprised to see her level change "so drastically" and would have to re-watch the match to understand where it all went wrong.
She added that she was disappointed by her overall performance at hardcourt majors this year after exiting the Australian Open in the fourth round as well.
"I don't really know what happened with my game. I felt no control suddenly. I just have to watch and see because, yeah, I didn't really know why I started making so many mistakes," she said.
Ostapenko faces a tough challenge against an in-form Gauff, whom she beat in the fourth round of the Australian Open earlier this year.
"She's a great young player, I played against her this year in Australia. It was a tough match," said Ostapenko.
"Of course, it's going to be another tough match. I don't expect any easy matches here at the Grand Slams. So I'm ready for another battle."
