It was a routine victory for the men in green and gold, but the Celtic playmaker looks in danger of being axed after struggling to prove his fitness
First-half goals from Oliver Bozanic and Adam Taggart were enough to clinch the win against the Brazilian second-tier outfit at the Arena Unimed Sicoob.
Attacking midfielder Rogic, who struggled for form and fitness on loan at Melbourne Victory in the second half of last season, started the game but only lasted until the break, feeling his groin and struggling to get around the pitch.
It looks likely the 21-year-old could be one of four players to miss out when head coach Ange Postecoglou names his final 23-man squad on Tuesday.
The Socceroos now look to the game against Croatia this Friday (Sat, 9am AEST) in Salvador in their final hit-out on Brazilian soil before their World Cup kicks off on June 13 against Chile.
With Luke Wilkshire as captain, Australia's structure looked good early and it was no surprise when the Socceroos took the lead against Parana.
Dario Vidosic supplied the assist down the left for his fellow Swiss-based player Bozanic to open the scoring early in the first half.
Both teams soon took a drinks break in the hot conditions but the Australians didn't relent after the restart.
Goalkeeper Eugene Galekovic was called into action from a set-piece before the Socceroo skipper set up Taggart brilliantly for the Jets striker to finish from inside the box to double the advantage around the half hour mark.
With both full backs pushing forward constantly, the Socceroos were dominating as they went into the main break 2-0 up.
The second half resumed with James Troisi on for his fellow Victory loanee Rogic.
Troisi was soon into the action, forcing a save low down to the left by the Parana keeper on 54 minutes.
A reshuffle in the Socceroos' structure saw Matt McKay move into midfield and Bozanic go to left-back as Australia continued to push for a third.
Two long-range efforts by Parana failed to threaten Galekovic's goal as the game moved into the final 20 minutes.
Troisi was again threatening with a neat one-two on the edge of the box but his shot was blocked as the game began to open up.
Massimo Luongo had a low shot saved and shortly after that midfielder James Holland came on for the hard-working Vidosic as the game entered its final 10 minutes.
Troisi again engineered some good lead-up play and almost put through the dangerous Taggart in the shadows of full-time, but a third goal wasn't to be.
The line up for the Socceroos:
Galekovic, Wilkshire, McGowan, Wright, McKay, Bozanic, Luongo, Vidosic (Holland), Halloran, Rogic (Troisi), Taggart.