Mithali paced her innings well and was involved in a significant partnership with Hemlata Kala as the pair held the Indian innings together to romp home with seven balls to spare.
Mithali, who captained the side in absence of regular captain Mamtha Maben, led from the front admirably to stay there till the end with an unconquered 92 which came off 144 deliveries.
All-rounder Hemlata Kala entertained the crowd as she struck two sixes in her knock of 41 consuming 70 deliveries.
Earlier, Indian bowlers pegged away to a tight line and length to restrict Australia to 184 for 7 off their stipulated 50 overs.
Lisa Sthalekar top-scored for the Aussies with a fine 43. Australian captain Belinda Clark chipped in with 35 while Lisa Keightley notch a handy 23.
For India Neeta David and Jhulan Goswami picked up two wicket apiece while Noshin-Al-Kadeer grabbed one wicket.
Mithali Raj was named Woman of the Match.
Despite the defeat, the Aussies lead the seven-match series 4-2. The final ODI will be played in Chennai on December 28.