Charismatic fourth seed Li demolished junior champion Ana Konjuh 6-2, 6-0, handing the 16-year-old a tennis lesson as she sets about ending her tournament jinx.
Li has made the final at Melbourne Park twice before, leading both times before being overcome by Kim Clijsters in 2011 and Victoria Azarenka last year, and is determined to go one better this time round.
“I always love coming to Melbourne.” she said. “I’m feeling good and feeling healthy.”
Her easy win set up a second-round clash with another qualifier in Swiss Belinda Bencic, who beat Japanese veteran Kimiko Date-Krumm, 43 and 27 years her senior, in three sets.
Li is in line to meet world number one Serena Williams in the semi-finals, with the five-time Melbourne champion getting her campaign underway Monday evening against Australian youngster Ashleigh Barty.
Defending champion Azarenka plays on Tuesday.
Also through was Germany’s Kerber, who had a second-set wipeout before bouncing back to overcome Australian Jarmila Gajosova 6-3, 0-6, 6-2.
She next faces Russian Alla Kudryavtseva.
But it was curtains for seven-time Grand Slam champion Venus Williams, who fell in a marathon clash against Russian 22nd seed Ekaterina Makarova.
The former world number one was unseeded despite playing 11 events last year and making three semi-finals, and she looked on course for victory after winning the first set.
But a series of unforced errors and failure to convert crucial break points cost her dearly and she was sent packing 2-6, 6-4, 6-4 after a nearly two-and-half-hour epic.
“Obviously losing any match is never any fun, especially in a major. So definitely would have wanted a different result,” said Williams.