Abby Bishop top-scored for the game with 21 points to go with seven rebounds, while Marianna Tolo, Elyse Penaluna and Tess Madgen all finished with 9 points each.
For the Swedish side, Louice Halvarsson finished with 20 points, while Elisabeth Egnell and Frida Elderbrink both ended up with 10 points apiece.
Only one point separated the sides at the half, with Sweden ahead 29-28 after a close battle in the first two quarters.
Sweden broke clear in the third, thanks to the work of Egnell who made a couple of big plays early in the period, before the likes of Loyd and Elderbrink rallied around her.
Sweden took a seven point lead heading into the final term, and threatened to steal the game.
But the Aussies lifted dramatically in the last quarter, led by Abby Bishop, who piled in 11 fourth-quarter points, as they clawed their way back into the contest. And when Bishop scored in the paint and converted the bonus free-throw, the Australians hit the lead with only 2.46 to play in the game.
They continued to attack and exploit their size advantage, getting to the foul line at will late in the game with Cumming, Hunt, Tolo and Bishop all managing to draw shooting fouls, the Aussies converting to ultimately take the win and the Bronze medal.
“We wanted gold so bad but this is still a great achievement. We are third best in the world in a competition that is basically under-25s so we are happy with that,” said Abby Bishop.
On her final quarter, Bishop said that it wasn’t necessarily the game plan to get her the ball late in the contest, but the fact that her teammates looked for her when the game was there to be won is a good feeling.
“It’s good to know that the girls have such confidence in me,” she said. “
“I am a confident player and I want the ball all the time, so for them to get me the ball in the fourth quarter with the game on the line suits me just fine,” she said.
Although gold was the objective, the side was pleased to seal the win and the bronze medal, over a side that proved to be a legitimate adversary for the star-studded Australian side.
“Sweden play tough, but we have an advantage because we are taller than them. We boxed them out in the second half and got more rebounds, which turned the game around,” said Aussie guard Tess Madgen.
“We absolutely did a great job. We only lost one game all tournament and that was to the USA and we won a bronze medal — that is amazing,” added Nicole Hunt.
Australia 66 (Bishop 21, Tolo 9, Penaluna 9, Madgen 9) def Sweden 56 (Halvarsson 20, Egnell 10, Elderbrink 10)