Shnaider is a freshman at North Carolina State University in the United States but the bandana-wearing left-hander, who possesses a ferocious forehand, has shown in Melbourne she can compete with the very best.
She had come through three rounds of qualifying before winning in straight sets on her Grand Slam main draw debut to set up the meeting with Sakkari, pushing the Greek all the way in a two-and-a-half-hour encounter.
"She is very young and very promising, maybe she should consider not going to college and turning pro," joked Sakkari, who is a two-time Grand Slam semi-finalist.
"It is difficult when you have not played someone before and I was hesitant. She was swinging hard and playing aggressively. I tried to find solutions and that's what I think I'm good at.
"It was a very high level from both of us."
Earlier, Petra Kvitova, the 2019 finalist and 15th seed, became the first top-20 seed to fall, losing 7-5 6-4 to Ukraine's Anhelina Kalinina.
American seventh seed Coco Gauff beat Britain's Emma Raducanu and compatriot Madison Keys, seeded 10th, won 6-3 6-2 against China's Wang Xinyu.
Wimbledon champion Elena Rybakina took just 59 minutes to beat Kaja Juvan of Slovena 6-2 6-1 and set up a meeting with Danielle Collins, who finished runner-up to Ashleigh Barty in Melbourne last year.
American Collins fought past Czech Karolina Muchova 6-7 (1-7) 6-2 7-6 (10-6) but mistakenly celebrated too early in the match tie-break, not realising it was first to 10 points rather than seven.
There was also a win for two-time champion Victoria Azarenka, with the Belarusian thrashing Nadia Podoroska of Argentina 6-0 6-1.
However, former US Open champions Sloane Stephens and Bianca Andreescu both lost. American Stephens fell 7-6 (7-2) 6-4 to Russia's Anastasia Potapova, while Canada's Andreescu was beaten 2-6 7-6 (9-7) 6-4 by Spanish qualifier Cristina Bucsa.
Play was initially delayed by six hours on the outside courts because of rain, with matches taking place late in the evening to make up for the schedule disruption after downpours had also forced postponements on day two.
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