Gibson trumped American Ann Li in straight sets, 6-1 6-4, to join compatriots Kimberley Birrell and Ajla Tomljanovic as first-round victors in California on Wednesday (Thursday AEDT).
Birrell, who bounced back into the top 70 in the world with her semi-final appearance last week at the WTA's ATX Open in Texas, accounted for Russia's Oksana Selekhmeteva.
The world No.69 won 6-1 6-4 while Tomljanovic, who Birrell defeated in a quarter-final in Austin before losing her semi to fourth-seeded Peyton Stearns, downed Romania's Elena-Gabriela Ruse 7-5 6-2 in the WTA 1000 tournament.
Storm Hunter meets Poland's Magdalena Frech in a first-round encounter on Thursday (Friday AEDT).
Australia's top-ranked female Maya Joint, the world No.29, has a bye before playing either Romanian Jaqueline Cristian or Indonesian Janice Tjen in the second round.
Joint's path forward would feature a round-of-32 encounter against world No.1 Aryna Sabalenka if both progress.
But while the trio of Australian women enjoyed first-round success, the nation's men's players largely struggled on the opening day of the corresponding ATP 1000 Masters event in  Indian Wells.
Only Adam Walton banked a first-up win - he downed Frenchman Quentin Halys 6-3 6-3 - as fellow Aussies Alexei Popyrin, James Duckworth, Chris O'Connell and Tristan Schoolkate all suffered losses.
American Jenson Brookson beat Popyrin 6-3 6-4, while Hungarian Morton Fucsovics prevailed over O'Connell 7-5 6-3.
Schoolkate was tipped out in a hard-fought encounter with Dino Prizmic - the Croatian triumphing 7-6 (7-5) 3-6 7-5.
Australia's top-ranked male player, world No.6 Alex de Minaur, will open his campaign in the second round against either Sebastian Korda or Francisco Comesana.
A potential Australian Open quarter-final re-match against Spain's world No.1 Carlos Alcaraz is on the cards should they reach the last eight.
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