Fifth-ranked American Pegula fired a career-high 16 aces to come up with a 7-6(2), 4-6, 7-5 victory in the must-win match against Wimbledon champion Noskova.
Her triumph, in the final group one round-robin match, meant world number four Gauff was eliminated from the elite season-ending event despite her gritty 6-4, 7-5 victory over Ukraine's Marta Kostyuk.
"Linda's such a great player," Pegula said. "Every time we've played, if you see the scoreline of our past matches, it's literally the same match every time... I knew I was going to get my chances.
"I felt like I did in the second, but then, you know, she's a Grand Slam champion, she's a great player and she did a great job to turn the match around.
"And then I had to do the same in the third," she added.
Noskova had already secured her semi-final spot with a pair of round-robin wins and she was on the brink of finishing with a perfect group record with a match point at 5-4 in the third.
Pegula escaped, firing an ace on game point, then broke Noskova in the next game. She closed out the win on her first match point.
Pegula finished second in the group behind Noskova and on Saturday will face group two winner Mirra Andreeva - just a week after a microphone installed to capture "ambient sound" on a practice court caught Pegula describing the Russian teen as a "diva".
Andreeva said after her opening match that Pegula had reached out to apologise and she considered the matter closed.
