Sunni Muslims Ahmed Mohamed, Abdullah Chaarani and Hatim Moukhaiber set fire to a Shi'ite mosque in a suburb of Melbourne.
Two had plotted an attack in central Melbourne just weeks later and were convicted of conspiring to plan a terrorist attack last year. They had bought machetes and explosives and tried to get a gun license before they were arrested, according to media reports.
The three have yet to be sentenced.
Australia, a staunch U.S. ally that sent troops to Afghanistan and Iraq, has been on heightened alert for attacks by home-grown militants returning from fighting in the Middle East or their supporters.
Last year, a Somali-born man set fire to a pickup truck laden with gas cylinders in the center of Melbourne and stabbed three people, killing one, before he was shot by police.Earlier this month, an Australian court found a man guilty of plotting to blow up a an Etihad Airways flight out of Sydney under the orders of Islamic State.