With Sylvain Guintoli winning his home race, Marco Melandri and Briton Tom Sykes remained in the fight for the WSBK crown with podium finishes.
Melandri stands 18.5 points behind his Italian compatriot after finishing second while Sykes, who led with nine laps remaining in the 23-lap race but faded to third by the end, is only 14.5 points off top spot.
With 25 points available for the winner, should Sykes claim race two Biaggi would have to finish fifth to secure the title.
Biaggi lost control on lap three at the Adelaide hairpin but Sykes could not fully capitalise, running wide to allow Guintoli and Melandri through.
He was pleased with the outcome, however.
"You have to finish the race and that's what counts," he said.
"It was shame that Biaggi made a mistake and I wasn't able to fully capitalise but we finished on the podium and we have one more race to do something about it.
"There's still a chance and hopefully we can make it happen in race two."
Briton Jonathan Rea had at one point looked a good bet for victory but high-sided on lap 12 ahead of Sykes.
Their compatriots Chaz Davies and Leon Camier also crashed out, along with Carlos Checa among others.