Roger Federer eased into the third round of Wimbledon to equal American legend Jimmy Connors's record of 17 appearances in the last 32.
Sam Stosur had no answer to Angelique Kerber's power as the German fired 15 winners in a 6-4, 6-4 victory.
Reigning Wimbledon champion Angelique Kerber was knocked out of Roland Garros in the first round on Sunday.
Angelique Kerber won 1-6, 6-2, 7-5 (7/4) in a tough encounter against Barbora Strycova.
Anastasia Pavlyuchenkova beat Sloane Stephens 6-7 (3/7), 6-3, 6-3 to set up a last eight clash with Danielle Collins.
Serena Williams won her 23rd title and seventh at Melbourne Park while eight weeks pregnant two years ago.
Simona Halep takes the top seeding among the women courtesy of her world number one ranking.
To win the decisive tie-break, a player will need to be the first to 10 with an advantage of at least two points.
Roger Federer became the first player to win three Hopman Cups, teaming with Belinda Bencic for the duo's second consecutive title.
World number two Angelique Kerber was too good for the 15th-ranked Barty in the opening match, winning 6-4, 6-4.
The 37-year-old kept his unbeaten record this week intact against the 15th-ranked Stefanos Tsitsipas.
Caroline Wozniacki and Angelique Kerber suffered shock defeats at the hands of less fancied opponents.
World number two Caroline Wozniacki and Wimbledon champion Angelique Kerber eased through their opening matches at the Wuhan Open in China on Tuesday.
Romania's Simona Halep continued to lead Women's Tennis Association (WTA) rankings released on Monday, ahead of Denmark's Caroline Wozniacki.
Roger Federer will be seeking a 13th appearance in the US Open quarter-finals when he plays Australian John Millman.
Sharapova needed just 66 minutes to see off 12th-seeded Kasatkina in an impressive and timely display of big-hitting with the US Open getting underway in just under three weeks' time.
Serena Williams is seeking to regain her top form after missing most of the 2017 WTA season due to a pregnancy.