Simona Halep awaits either Dutch seventh seed Kiki Bertens, a finalist in Madrid last year, or 2017 US Open champion Sloane Stephens in the final.
Japan's Naomi Osaka retained the world number one spot.
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.
Serena Williams thumped dangerous Swiss teen Belinda Bencic 6-4, 6-3 to enter the second round of the Australian Open.
David Ferrer, the 13th seed,
Venus Williams defeated Maria Sakkari 7-5, 4-6, 6-3
Jelena Jankovic came from a set down to beat Belinda Bencic 4-6, 7-5, 6-4 in the Dubai Open first round.
Martina Hingis and her partner Belinda Bencic needed just over an hour to seal their 6-3, 6-2 win over Germany's Andrea Petkovic and Anna-Lena Groenefeld.
Roger Federer is also set to play men's doubles with Stan Wawrinka in 2016 Rio Olympics while Martina Hingis will play women's doubles with Belinda Bencic.
Agnieszka Radwanska's victory in the WTA Pan Pacific Open has propelled the Polish player back in the world's top 10.
Beaming with confidence, the eighth seed will carry her incredible momentum into the match against the experienced Pole, whom Bencic beat in June in the final of the Aegon International in Eastbourne, the first WTA title for the youngster.
Here's a list of players who can break out and make a name for themselves during the US Open 2015 tournament.
The victory is Belinda Bencic's first premier-five level title and second WTA title. She also earns her $456,000 first place prize, her biggest payday of her professional career. After two long sets that lasted over an hour each, Simona Halep was forced to retire in the third set due to a left leg injury and heat exhaustion
Belinda Bencic at 18 is the youngest player to beat Serena Williams, 33, since she lost to a 17-year-old Maria Sharapova at Wimbledon in 2004.
Swiss Belinda Bencic, 18, defeated fifth seed Ana Ivanovic 6-4, 6-2 to record her fourth win against a top-10 ranked player this season.
Belinda Bencic defeated Agnieszka Radwanska to win the first title of her career at Eastbourne. Bencic was coached part-time by Martina Hingis and by Hingis's mother Melanie Molitor.
Belinda Bencic, 18-year-old Swiss, denied Agnieszka Radwanska a second title at Devonshire Park on the English south coast in a contest which lasted over two hours.
