China's fourth seed blasts into the second round but former great Venus Williams crashed out in the blistering Melbourne heat
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.
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Li Na and Venus Williams. Pic/ AFP
"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.
"I think my error count was a little high. I haven't looked at the stats yet, so I don't know what the errors were or the first?serve percentage was. I have to look at that and just kind of evaluate the match."
Williams hasn't won a Grand Slam since Wimbledon in 2008 and is without a title since Luxembourg in October 2012, although she made the final of the warm-up Auckland International, losing to Ana Ivanovic.
The American suffers from the energy-sapping Sjogren's Syndrome and she appeared to wilt in the hot conditions as the match wore on.
After showing some glimpses of the Williams of old in the first set with some sizzling backhand winners, she blew a chance to go 5-2 up in the second by failing to convert two break points.
It cost her dearly with Makarova bouncing back to take the set and ultimately the match to line up a second round clash with American Irina Falconi, who beat Spain's Anabel Medina Garrigues.
In contrast, Li was always in charge against Kunjoh, who was making her Grand Slam debut after winning the Australian Open girls' title last year.
Li rattled through the match, giving the teenager a lesson and escaping the court with minimum effort as temperatures climbed to 30 Celsius (86 Fahrenheit), with 40-plus Celsius forecast on Tuesday.
It was an impressive start for Li, who reached the season-ending WTA Championships final last year and started 2014 with victory at the Shenzhen Open.
But she would not have been competing at all if she had gone through with a threat to quit last year.
The charismatic Chinese told the Melbourne Age that she almost didn't play Wimbledon and considered retirement after a second-round defeat at Roland Garros and a quarter-final loss at Eastbourne, which forced her to consider retirement.
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