Zheng, the 12th seed, outlasted Wang Yafan in an epic all-Chinese battle on Rod Laver Arena on Saturday, winning 6-4 2-6 7-6 (10-8) after a 83-minute match tiebreaker.
Zheng Qinwen, left, overcame fellow Chinese Yafan in the Australian Open third round. (Joel Carrett/AAP PHOTOS)
Ten years ago, Li became the first Asian woman to win the Australian Open crown, following her 2011 French Open title, with the now 41-year-old returning to Melbourne a decade on to compete in the Legends tournament.
Zheng, 21, said she clearly remembered Li's victory at Melbourne Park, beating Slovak Dominika Cibulova 7-6 (7-3) 6-0 in the final.
"Of course, cause I was sitting there in front of TV and I watch from the beginning until the end and that final, I've watched it more than 10 times so I have a lot of memories," said Zheng, who reached the quarter-finals of the US Open last year.
"She's an unbelievable player - the first Asian woman who was the grand slam champion - how can you not remember that."
Zheng will next face Oceane Dodin, who downed fellow French player Clara Burel 6-2 6-4.
Ukrainian qualifier Dayana Yastremska is through to the Australian Open's fourth round. (Lukas Coch/AAP PHOTOS)
Meanwhile, Ukrainian Dayana Yastremska continued her inspired run from qualifying to advance to the fourth round for the first time.
Yastremska upset American 27th seed Emma Navarro 6-2 2-6 6-1 in the opening match of day seven.
The 23-year-old was joined soon after by Russian Anna Kalinskaya, who won a tough tussle with American Sloane Stephens 6-7 (10-8) 6-1 6-4.
Veteran Stephens, who was an Open semi-finalist back in 2013 and won the US Open in 2017, called for some sushi and smoothies to be delivered to her on court mid-match.
But it didn't provide the energy boost she was looking for against the world No.75.
Before this year Kalinskaya, 25, had never previously won a match at Melbourne Park.
She will next take on the winner of a clash between another Russian Anna Blinkova and Italian 26th seed Jasmine Paolini.
Yastremska's reward is a crack at either two-time champion Victoria Azarenka or in-form 11th seed Jelena Ostapenko on Monday for a surprise berth in the quarter-finals.
Azarenka, a semi-finalist last year and champion in 2012 and 2013, takes on the newly crowed Adelaide International winner Ostapenko later on Saturday.
World No.1 Iga Swiatek is playing Czech Linda Noskova in the night session.
20°C