John Patrick Casey, now 76, had pleaded not guilty to three counts of sexual assault against a person under the age of 16.
After deliberating for almost nine hours, a jury on Wednesday found Casey guilty of sexual assault and an act of indecency involving a person under the age of 16.
It was unable to reach a verdict on two other charges relating to the incident, which took place in his home at Mallanganee in northern New South Wales.
Casey was the parish priest at Mallanganee between 1981 and 1988.
The crown prosecutor told the court Casey had taken the complainant and a friend out for day trips, weekends away and a sleepover at his home.
The jury heard Casey often let the pair drink alcohol and smoke cigarettes.
The crown alleged that during the overnight stay at his house, the priest performed an indecent massage on the complainant, who became scared to stay overnight at the priest's house and never went back.
The court heard the complainant never spoke to his friend about what allegedly happened to him, and did not go to the police about it until he was 52 years old.
Casey pleaded not guilty, and while on the witness stand denied any wrongdoing.
But during closing statements, the Crown prosecutor described the complainant as a credible and honest witness.
"People aren't mistaken about sexual assault," she said.
"It either happened and they're being honest about it, or they're lying."
Defence barrister Jason Watts argued that the differences between the evidence given by the complainant and his friend about what happened at the presbytery, combined with Casey's evidence, meant the alleged abuse could not have occurred.
He also warned the jury against bringing any prejudice or sympathy to their decision making.
"If because of events happening … around the world over the last 20 years, you have some preconceived notions about Catholic priests, you wouldn't allow those to interfere with your reasoning in this case," he said.
The jury could not reach a verdict on two similar charges involving sexual assault and an act of indecency.
Casey had his bail continued, and the matter will return to court in December when the Office of the Director of Public Prosecutions will announce whether it will go ahead with a retrial of the two remaining charges.