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.
Serena Williams moved up one spot in the WTA rankings this week to world No.27.
Novak Djokovic won his fourth men's singles title while Angelique Kerber became the first German in 22 years to win the women's crown.
Serena Williams' husband Alexis Ohanian on Saturday posted a heartfelt message on his Instagram account following the tennis star's loss to Angelique Kerber in the final at Wimbledon.
Angelique Kerber became the first German woman to win Wimbledon for 22 years.
Wimbledon Women's Final highlights, Serena Williams vs Angelique Kerber Tennis Match: Angelique Kerber became the first German to win a Wimbledon singles title since Steffi Graf in 1996.
Serena Williams is on the verge of making more history as the seven-time champion aims to become the first mother to win Wimbledon since 1980.
Kerber took the express route to her a fourth Grand Slam title match with a 'blink and you miss it' demolition.
Angelique Kerber and Elina Svitolina will face off in a Dubai Championships semi-final on Friday after both ran down opponents in quick straight-sets wins.
Top seed Simona Halep was impressive on Rod Laver Arena in thumping sixth seed Karolina Pliskova 6-3, 6-2, reeling off nine games in a row after going 0-3 behind in the first set.
Second seed Federer will now play fellow veteran Berdych, a semi-finalist in 2014 and 2015 at his most successful major, who demolished Italy's Fabio Fognini 6-1, 6-4, 6-4.
Roger Federer and Novak Djokovic kept up their relentless march towards a semi-final meeting at the Australian Open Saturday
Maria Sharapova was sent crashing out of the Australian Open in a crushing defeat by Angelique Kerber Saturday as Simona Halep survived a titanic struggle to make the last 16.
Milos Raonic was stunned by Lukas Lacko in the first round of the tournament.
It was the first time an Australian woman featured in the Sydney International final since 2005 when Alicia Molik took the title over Sam Stosur.