Latif, making her Commonwealth Games debut, combined for a personal best total of 152kg.
It was the same as the Seychelles' Clementina Agricole, but enough to secure third because of Latif's lighter body weight.
It was Australia's second medal from as many women's events following Brisbane teenager Erika Yamasaki's bronze in the 48kg category on Wednesday.
"I gave up a lot for this, I gave up my job to train for this, I've had no money since then," a delighted Latif said. "It's all paid off, I'll go back to Sydney at the end of the games and start working again."
Latif's achievement was overshadowed by a titanic struggle between Papua New Guinea's Dika Toua and eventual gold medallist, Canadian Maryse Turcotte, that saw both competitors set Commonwealth Games records before Toua was injured during an unsuccessful attempt to clean and jerk 108kg.
Toua required medical treatment when the bar fell on her right leg.
The 21-year-old returned, but failed to lift 108kg with her final attempt, ensuring Turcotte etched her name into the Games record books when she combined for 188kg, 7kg better than Indian Chanu Sanamacha's Manchester mark.