Roger Federer produced an excellent all-round performance despite being tested by the world number 103 Filip Krajinovic.
Venus Williams rallied from a set and two breaks down to topple third-seeded Petra Kvitova 4-6, 7-5, 6-4 at Indian Wells.
Serena Williams won her 23rd major Down Under two years ago while two months pregnant.
Novak Djokovic defeated Jo-Wilfried Tsonga 6-3, 7-5, 6-4 in straight sets.
The pressure on the reigning French Open champion will only increase in her next round.
Serena Williams won her 23rd title and seventh at Melbourne Park while eight weeks pregnant two years ago.
The family of 78-year-old Jerome Barson had filed a wrongful death suit against Williams following the June 2017 crash in Palm Beach, Florida.
Serena Williams was all business for the highly anticipated all-Williams clash under the lights on Arthur Ashe Stadium.
Serena Williams enjoys a 17-12 head-to-head superiority against her sister Venus.
Top seed Halep took no prisoners against Williams, blitzing the 38-year-old American 6-2, 6-2 in just 71 minutes to reach the quarter-finals.
Maria Sakkari won 6-4, 7-6 (7/2) against former world number one Venus Williams.
Kiki Bertens, who reached the French Open semi-finals in 2016, had never before been past the Wimbledon third round.
Roger Federer delivered a Centre Court masterclass lasting 89 minutes as the Swiss star hit 48 winners and 16 aces in his 6-4, 6-4, 6-1 victory.
In all the four Slams, it's only the sixth time in the Open era that the defending champion has perished at the first hurdle.
Seven-time major winner Venus Williams suffered back-to-back opening-round exits at the Slams for the first time in her 21-year career.
Serena and Venus Williams have won 14 Grand Slam doubles titles as a team.
Simona Halep needed to reach at least the last eight and go further than world number two Caroline Wozniacki to retain the top-ranking going into the French Open.
Venus Williams showed no signs of fatigue to power home 5-7, 6-1, 6-2 in two hours and 19 minutes.