The women's victory on Sunday also allowed the visitors to reclaim the number one spot on the ICC rankings.
Meg Lanning elected to bat after winning the toss and Australia set the pace with an innings of 7-332.
Healy managed to dig in after quickly losing fellow opener Nicole Bolton (11) and then Meg Lanning (18), reaching 133 off 115 balls before being caught off a Poonam Yadav delivery.
Rachael Hayes' 43 and a rapid 34 from Beth Mooney helped push Australia to a total over 300.
India made a fast start to the chase, reaching 0-101 before two wickets in as many balls to Ashleigh Gardner (3-40).
Jess Jonassen and Nicola Carey then claimed the key wickets of Mithali Raj (21) and Harmanpreet Kaur (25).
Although Deepti Sharma (37) and Sushma Verma (29) did their best, the tail was ably cleaned up by Megan Schutt (2-54) and Ellyse Perry (2-40).
Healy said accomplishing her maiden ton was "a big feeling of relief".
"I've played a lot of cricket to not have one so I'm pretty excited to sit here finally with a 100 under my belt and hopefully I can get a couple more before I pull up stumps," Healy said.
"[Scoring 300] is a goal for us to consistently hit that mark and we did it quite comfortably in the end today.
"We've just got so much power right down our batting order, which is really exciting."
Following the series win, Australia returns to Mumbai for the Twenty20 tri-series with England and India, which starts on March 22.