Australian duo Ajla Tomljanovic and Daria Kasatkina progressed after contrasting matches on Monday's opening day of the WTA 500 tournament in Adelaide.
After 17-year-old compatriot Emerson Jones exited with a straight-sets loss, Russian-born Kasatkina prevailed against Greek wildcard Maria Sakkari 7-6 (7-2) 6-4 in a night clash on centre court.
World No.48 Kasatkina took 70 minutes to claim the opening set, and another 45 minutes to win the second against Sakkari, who was ranked third in the world in March 2022 and is currently 52nd.
Earlier, Tomljanovic advanced when injury-hit Dane Clara Tauson retired after one set.
Tomljanovic won the set in a tiebreak, 7-6 (7-5) and Denmark's world No.14, who played with a vertical bandage on her left hamstring, then sought medical treatment before retiring.
The extent of her injury not immediately known ahead of the Australian Open starting on Sunday.
"It's really unfortunate when someone has to retire. I know what it feels like, it's never easy," the 32-year-old Tomljanovic said.
"But just from my point of view, that whole set I was very locked in and didn't really see what was going on with her and what was bothering her."
Tomljanovic could meet rising compatriot Maya Joint in the second round. The world No.32 and Australia's top-ranked woman meets American Sofia Kenin in a first-round clash on Tuesday.
The winner will play Tomljanovic, who was given a wildcard into the tournament and wants to improve on a performance against Tauson she rated as "a bit scrappy".
"I don't think it was a cleanest set for me," Tomljanovic said.
"I couldn't really find my range; it was either in the fence or in the net so I was getting a bit frustrated with that.
"But the longer the match was going, the more I was finding it and I was looking forward to playing the second set. I could feel I could play better."
Earlier on Monday, Australia's 17-year-old wildcard Jones was outclassed in straight sets by American sixth seed Emma Navarro.
World No.15 Navarro triumphed 6-3 6-3 and made decisive inroads when receiving against the young Australian, who won just six of 24 points on her second serve.
"I didn't play my best tennis ... I was a bit flat," Jones said.
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