Six-time men's champion Novak Djokovic won his opening match under the lights, beating Bernard Tomic 7-6 (2), 6-2.
Azarenka, a former world number one now ranked 48th in the world, said she started a little too passive in dropping the first two games against her fellow Belarussian, but roared back to seal the win.
The sisters share 14 Grand Slam doubles championships combined.
The 23-time major champion could end up facing former World number one Victoria Azarenka in a second-round match
The Duchess of Sussex, due to give birth in the spring, returned to Britain Thursday after enjoying a party with celebrity friends at what British papers referred to as the most expensive hotel suite.
Pliskova survived four match points and bounced back from 1-5 down in the third set to defeat Williams for a spot in the final four.
Williams' bid to claim her 24th Grand Slam title was ended by the seventh seed, who will now face Naomi Osaka in the semi-final.
Pliskova done it before at a Grand Slam when she defeated Williams in straight sets in the 2016 US Open semi-finals.
The 37-year-old American stormed past top seed Simona Halep to reach the quarter-finals at the Australian Open on Monday, with the Romanian saying it felt like being "hit by a train".
Serna Williams beats Halep in an epic three-setter to set up a last eight clash with Czech eighth seed Karolina Pliskova.
Australian Open: Naomi Osaka sets up Elina Svitolina last-eight test, Serena Williams faces showdown
The victory left Osaka with a last-eight clash against ambitious Ukrainian Svitolina, who battled past American Madison Keys 6-2, 1-6, 6-1.
On day six at Melbourne Park, the Romanian finally hit form to pull off her best win of the year and cruise past the veteran American 6-2, 6-3.
Williams swatted aside Ukrainian teenager Dayana Yastremska 6-2, 6-1 in a Melbourne Park mauling that reduced the world number 57 to tears.
Australian Open: Serena Williams relentlessly marches on as Naomi Osaka, Elina Svitolina survive scares
Serena Williams, seeded 16, has dropped just nine games in her three matches so far and with face either sister Venus or world number one Simona Halep for a berth in the quarter-finals.
The 37-year-old won her 23rd major Down Under two years ago while two months pregnant and is the bookies' favourite to claim an eighth Australian title, despite being seeded 16th.