Britain's Raducanu is looking to make an impact in Seoul after a string of last-minute withdrawals, including world number one Iga Swiatek, US Open runner-up Jessica Pegula and former Wimbledon champion Elena Rybakina.
The 2021 US Open champion Raducanu, ranked 70th in the world, had to dig deep to beat her 48th-ranked opponent in steamy conditions in a match that lasted two hours 43 minutes.
"I'm proud to have made it through to the next round," said Raducanu, who is unseeded.
"Thank you to everyone for sticking around and watching us. It was tough, it was very humid, the balls were bouncing around a lot."
Raducanu's next opponent will be China's Yue Yuan, the eighth seed.
"It was a tough match to get through," added Raducanu.
"I haven't played many matches in the last few months and Peyton is a really good player in really good form, so I'm pretty pleased."
Raducanu, who has failed to build on her stunning US Open success, stormed into a 4-1 first-set lead but let her opponent come back before edging her in the tiebreak.
Raducanu struggled to shake off Stearns in the second set and could not finish the job when serving for the match at 5-3.
She had to battle some more to take the second set to a tiebreak but then rode a late surge of momentum to clinch the match in straight sets.
American Hailey Baptiste joined her in the second round after beating compatriot and former US Open champion Sloane Stephens 7-6(4), 6-2.
Sixth seed Yulia Putintseva of Kazakhstan was knocked out after a 6-3, 7-6(5) loss to American Amanda Anisimova.
Play was delayed for 45 minutes at the start of the day for excessive heat.
