The 33-year-old overcame early breaks of serve in both sets to win 6-3 6-2 in the tournament's first match on Pat Rafter Arena on Sunday against Trevisan, who peaked at No.18 in the world in May.
Rodionova, the world No.114, is Australia's highest-ranked female and needed a wildcard to feature in her first top-level event in nearly two years.
She has worked tirelessly to get back, overcoming a wrist injury in 2022 and then dominating on the lower-tier ITF level this year to surge from back from No.302 in the world.
Rodionova has won a staggering seven ITF singles titles and 78 matches this year and will now face former Australian Open champion Sofia Kenin, of the US, in the second round.
This Brisbane International has not been held as a men's and women's event since 2019.
Bumper New Year's Eve crowds were queueing before gates opened on Sunday morning to celebrate its return.
"I had so much fun today - I don't remember the last time I enjoyed being on the court so much," Rodionova said.
"I was out for eight months. It was a tough time and I started back last year, played over 100 matches (this year) and am now feeling really confident on court.
"Don't take it (your health) for granted - I think you can see I'm really having fun out here."
Czech player Katerina Siniakova faces American Sloane Stephens in the next women's fixture, before an all-Australian clash between Alexei Popyrin and Chris O'Connell  headlines the main court action later on Sunday.
Andy Murray and Rafael Nadal will also play in separate doubles matches before featuring in singles on Monday or Tuesday.
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