A month after being the only Australian to successfully qualify at Roland Garros, and then winning her first-round match on the Paris clay, Hunter edged a step closer to making the Wimbledon main draw.
The left-hander beat Brit Mingge Xu 7-5 6-4 on the Roehampton grass courts to set up a second-round tussle on Wednesday with Russian top seed Elina Avanesyan.
Like in Paris, Hunter will need to survive three sudden-death matches to qualify for the London grand slam.
Jaimee Fourlis, Olivia Gadecki and Priscilla Hon also won their opening qualifiers on Tuesday.
Fourlis beat Slovenia's Polona Hercog 6-3 4-6 6-3 and next faces Slovakian Viktoria Hruncakova on Wednesday.
Gadecki outclassed American teenager Katrina Scott 6-3 6-4 to book a date with another US hopeful, Ann Li.
And Hon will play Italian Lucrezia Stefanini after downing Frenchwoman Amandine Hesse 6-2 6-3.
But Arina Rodionova lost 6-2 6-1 to German veteran Laura Siegemund and Kim Birrell bowed out with a 6-4 6-3 defeat to Ukraine's Dayana Yastremska.
Daria Saville, playing on an injury-protected ranking in her comeback from a torn ACL, is the only Australian so far in the Wimbledon main draw after Monday's withdrawal of two-time quarter-finalist Ajla Tomljanovic with a season-wrecking knee injury.
In other notable qualifying encounters, former Australian Open champion Sofia Kenin beat fellow America Irina Falconi Hartman 6-3 6-2, while Canada's 2014 Wimbledon finalist Eugenie Bouchard crashed out in the first round 6-4 7-5 to Belgian Greet Minnen.
Three Aussie men will also continue their qualifying pushes on Wednesday.
James Duckworth has a second-round meeting with Frenchman Harold Mayot, Marc Polmans plays American Zachary Svajda and Rinky Hijikata is up against Chile's Tomas Barrios Vera.
Duckworth, Polmans and Hijikata are hoping to boost Australia's eight-strong contingent in the Wimbledon men's singles main draw.
Queen's Club finalist Alex de Minaur is seeded 16th while last year's runner-up Nick Kyrgios will be unseeded if he lines up after playing only one match all year because of a knee injury.
The other Australians in Friday's draw will be Max Purcell, Chris O'Connell, Jordan Thompson, Jason Kubler, Alexander Vukic and Alexei Popyrin.
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