Then Megan Schutt starred with the ball, taking four for 18 as India were dismissed for just 99 in their final over.
The official attendance at Melbourne Cricket Ground of 86,174 was a world record for a women's cricket match.
Victory capped an emphatic turnaround by the Australians, who had suffered a 17-run defeat by India in the group stages of the competition.
From the moment Indian star Shafali Verma edged behind in the third ball of the chase, a different outcome appeared inevitable.
Australian captain Meg Lanning was quoted as saying by BBC Sport: "We've had everything thrown at us, we've had our ups and downs and scraped through the tournament but it was our best performance on the biggest stage."