The 23-year-old Navarro - who had never before been seeded this high at a major - overcame the disappointment of dropping the first set to triumph 6-7 (5-7) 7-6 (7-5) 7-5 in a match that lasted three hours and 20 minutes.
Navarro advanced to the semis at a grand slam for the first time at last year's US Open, before falling to eventual champion Aryna Sabalenka.
She extended her win-loss record against the feisty Stearns to 5-1 on Tuesday, but only after being pushed to the limit on her Rod Laver Arena debut.
Peyton Stearns lost no admirers in a gutsy display against Emma Navarro. (Joel Carrett/AAP PHOTOS)
"That was one of the more unique matches I've played in a while," Navarro said.
"I definitely did not have my best stuff today.
"I was just relying a lot on my grit and toughness and fight.
"(Stearns) had a lot of moments there where she could have maybe closed it out or run away with it."
Navarro, 23, is the daughter of billionaire US businessman Ben Navarro.
Her opponent in the second round will be China's Wang Xiyu, who beat Austrian Julia Grabher 6-1 7-5.
Former US Open champion Emma Raducanu put aside an interrupted build-up to book her spot in the second round at Melbourne Park.
The high-profile British player suffered a back spasm earlier in the month, then refused treatment for a painful ant bite a few days ago because of worries she could inadvertently ingest a contaminated substance.
Playing her first competitive match since November, Raducanu downed No.26 seed Ekaterina Alexandrova from Russia 7-6 (7-4) 7-6 (7-2) in a match featuring eight service breaks in the first set and 12 in total.
Emma Raducanu has booked her spot in the second round at Melbourne Park. (Lukas Coch/AAP PHOTOS)
Raducanu mixed nine aces with 15 double faults, but her serve held up when it mattered most in the second-set tiebreak.
Since becoming the first player - man or woman - to win a grand slam title after coming through qualifying at the 2021 US Open, Raducanu has had to deal with crippling levels of expectation in her home country.
Raducanu's victory set up an intriguing second-round clash with her American friend Amanda Anisimova, another player who has had to deal with the positives and negatives of fame at a young age.
"There are challenges in the sense of obviously you get a lot of attention," said 22-year-old Raducanu.
"Maybe certain decisions are judged, or what you're doing is potentially criticised.
"At the same time I feel like it's given us a great platform to be able to have opportunities, to be able to invest in our team, to be able to enjoy playing on big courts.
"So even though there comes challenges, I want to look at the positive and optimistic side as well."
Anisimova was largely untroubled in downing Argentina's Maria Lourdes Carle 6-2 6-3.
Amanda Anisimova will play Emma Raducanu in the second round. (AP PHOTO)
The American, who has been ranked as high as No.21 in the world, took a break from the sport in 2023 to deal with mental health issues.
The 23-year-old has also been the victim of vicious online trolling.
In other women's action on Tuesday, ninth-seeded Russian Daria Kasatkina made short work of Bulgarian Viktoriya Tomova, winning 6-1 6-3.
Big-hitting Madison Keys, the 19th seed, was too good for fellow American Ann Li, banking a 6-4 7-5 victory, while another American, wildcard Iva Jovic, ousted Spaniard Nuria Parrizas Dias 6-2 6-1.
Fourth-seeded Italian Jasmine Paolini swept past China's Wei Sijia, winning 6-0 6-4.
