The match was originally scheduled to be played at Optus Stadium, and hosted by the Perth Scorchers following their defeat in The Qualifier on Saturday night.
The BBL matches were moved following the closure of state borders due to COVID-19 concerns.
Yuzvendra Chahal had an eventful day with the ball on Friday as he finished with figures of 3/25, which included two prized wickets of Aaron Finch and Steve Smith.
The win in Canberra was India's ninth consecutive T20I win on the trot, with their first win going back to December 2019 against West Indies in Mumbai.
Hardik Pandya took to his official social media profile to share a picture with the Indian cricketers including captain Virat Kohli.
India, with their win at the Manuka Oval, now stand fourth in the points table with 10 points from three games. They had earlier lost in Sydney twice in this series against the Aussies.
Even though it was a dead rubber with Australia winning the first two ODIs in Sydney in identical fashion, the win was a massive relief for the visitors who still have a long summer to spend Down Under.
Electing to bat, India scored 302 for five with Hardik Pandya (92 not out) and Ravindra Jadeja (66 not out) rasing an unbeaten 150-run stand for the sixth wicket.
AUS vs IND, 3rd ODI: India (302/5) defeated Australia (289) by 13 runs in Canberra to avoid whitewash. The hosts clinched series 2-1.
Captain Virat Kohli couldn't feel more pleased praising about the manner in which his men scripted in a comeback when twice put under pressure by the hosts.
T Natarajan will become the 232nd player to represent Team India in ODIs.
As per the tentative schedule, the ODI series will begin on November 27, while T20Is start from December 4.
The Indian team was initially supposed to land in Brisbane but apparently Queensland state health authorities won't allow the visitors to train during the mandatory 14-day quarantine period.
At least 28 people have died and more than 2,000 homes have been destroyed across the country in bushfires. "We know that trauma and tragedy are deeply linked with mental health impacts and what we're seeing now is that people are in the early phases of recovery and response," Health Minister Greg Hunt said.
Prajnesh Gunneswaran secured a straight-set win but Ramkumar Ramanathan lost in the first round of the Canberra International.
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