Hunter upset Swiss eighth seed Viktorija Golubic 6-4 6-2 while Gadecki thrashed Latvian Darja Semenistaja 6-0 6-2 to progress to the second round of qualifying.
Fourlis battled valiantly for almost three hours on the slow red dirt to beat Andorran teenage prodigy Victoria Jimenez Kasinsteva 6-4 4-6 6-3.
Jimenez Kasinsteva won the 2020 Australian Open junior title at just 14 on her grand slam debut.
But she was unable to break Fourlis' spirit as the 23-year-old strives to make the main draw in Paris for the first time since being awarded a wildcard in 2017.
Hunter, Fourlis and Gadecki plus day-one winner Arina Rodionova all need to survive three rounds of sudden-death qualifying to join Australian wildcard Kim Birrell in the women's singles at Roland Garros.
Aleksandar Vukic and Marc Polmans also won their opening matches in men's qualifying.
Vukic, who has just cracked the world's top 100 for the first time, beat Belgian Raphael Collignon 6-4 4-6 6-4 while Polmans defeated Frenchman Harold Mayot 7-5 7-5.
Australia have seven confirmed starters so far in the men's main draw in Paris - world No.19 Alex de Minaur, Max Purcell, Jason Kubler, Jordan Thompson, Alexei Popyrin, Chris O'Connell and wildcard Thanasi Kokkinakis.
But James Duckworth, Alex Bolt and Priscilla Hon lost their opening qualifying matches on Tuesday.
The claycourt grand slam starts on Sunday.
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