Current world No 1 and former incumbent were both comfortable winners in Shenzhen as was the world No 6 from Ukraine over in Brisbane.
Halep and Sharapova make winning starts to 2018 as Svitolina sets sights on No 1 ranking
Maria Sharapova marked the start of her first full season back on the WTA Tour with a comfortable 6-3, 6-0 win over Romania's Mihaela Buzarnescu in the first round of the Shenzhen Open on Monday.
Five-time grand slam champion Sharapova hit 18 winners and needed just an hour and 22 minutes to defeat Buzarnescu. The 30-year-old Russian will face 2017 runner-up Alison Riske, who upset China's fifth seed Wang Qiang on Sunday.
"Every match gets tougher and as a competitor and someone who tries to be realistic, I like to only look ahead to the next opponent," said Sharapova, who returned to the tour in April last year following a 15-month doping suspension.
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"She beat a crowd favourite yesterday, so I know I have a tough match ahead, but I just want to keep playing better, and keep improving no matter who is across the net."
World No 1 Simona Halep was also comfortable in victory on Monday, hitting 12 winners en route to sealing a 6-4, 6-1 win over American Nicole Gibbs.
Romanian Halep, 26, set up a second round clash with China's Duan Yingying who defeated Evgeniya Rodina 6-2 7-5.
"It's always nice to play here in Shenzhen," said Halep, who captured the Shenzhen Open title in 2015. "It's my first victory this year as No 1 in the world, so I'm happy and enjoying the time."
Unseeded Danka Kovinic, ranked No 123 in the world, stunned Greek seventh-seeded Maria Sakkari 4-6, 6-2, 6-3.
Local hope Zhang Shuai powered past Russia's Anna Blinkova 6-3, 6-4 and was joined in the next round by Timea Babos who beat China's Wang Xiyu 6-1 6-1.
Over at the Brisbane International, Elina Svitolina got her season under way with an impressive 6-2, 6-4 win over former world No 6 Carla Suarez Navarro, and the Ukrainian immediately set her sights on the No 1 ranking.
Svitolina, 22, is currently ranked No 6 and enjoyed a break out 2017, winning five titles on her way to a career-high world ranking of No 3.
However, Svitolina has set her goals even higher, and after working hard in the off-season, believes she can reach the pinnacle of women's tennis.
"This match was a good example that I can play a good level of tennis, a high level of tennis," she said. "So I will try to continue to work and to just be focused on these kind of things.
"That's what's important for me - and then the grand slam and No 1 is all going to come if I have my game, if I'm healthy, if I'm playing my best."
Svitolina will take on Ana Konjuh in the second round following the Croatian's 6-1, 6-2 win over Dutchwoman Kiki Bertens on Sunday.
A miserable run by sixth-seeded Frenchwoman Kristina Mladenovic continued when she lost to Belarus qualifier Aliaksandra Sasnovich.
Mladenovic, who has not won a match since Wimbledon, raced through the first set before Sasnovich fought back to win 1-6, 6-3, 7-5.