Brazil were looking to boost their prospects of reaching the quarter-finals and had the Sapphires on the ropes late in the fourth quarter when Franciele Nascimiento's jump shot put the South Americans into a 75-71 lead.
The Aussies battled back to take the lead, only for another basket from Nascimiento, which took her personal points haul to 23 (she finished with a game-high 26 points), to level the scores at 77-77 with 2:37 remaining.
Kathleen McLeod passed to Camino, who connected from long range for an 80-77 advantage.
And after Roberta Fogaca made two free throws to close the gap to one for Brazil, Francis buried a three-ball for an 83-79 Australia lead and the team from Down Under held on.
Camino had 24 points to lead the Australians, who suffered a heartbreaking 90-88 defeat to the United States on opening day but have followed up that setback with victories over Hungary, Spain and Japan to clinch a place in the last eight.
Brazil, however, have just one victory with Wednesday's result leaving them on the outside of the quarter-finals.
If Spain and Japan also lose their games today and finish with 1-4 records, goal difference in the games between the sides will determine who advances to the quarter-finals.
Fifa World Cup