Captain Jodie Fields lost the toss and India sent Australia into bat in hot and humid conditions at Galle International Stadium.
Right-arm medium pacer Julie Hunter struck first for the Australians with Jess Cameron catching Anita Sharma (11) at mid-on. Cameron was safe hands again in the 6th over catching Poonam Rout at deep mid-on, off the blowing of Erin Osborne.
Left-armed spinner Jess Jonassen picked up her first wicket in the 12th over, dismissing big hitting batter Jhulan Goswami (2). Jonassen was the most economical of the Australian bowlers averaging two runs for her three overs and bowled a maiden.
Player of the Match Osborne claimed another two wickets late in the innings to finish with figures of 3-0-13-3.
Australia's great all-round bowling effort restricted the passionate Indians to a modest 104 runs for the chase.
In reply, Meg Lanning and Alyssa Healing got the Commonwealth Bank Southern Stars of to a cracking start combining for a 43 run partnership before Healy (21) was dismissed off the bowling of Shubhlakshmi Sharma.
Lanning contributed a classy 39 runs to the chase before she was dismissed by Goswami. Lanning has now become the first Women's T20 player to get scores over 30 in five consecutive T20 matches.
Cameron continued her superb form from the field, where she took three catches, to the crease hitting 36 off 35 to take Australia through to the win in the 17th over.
Fields said she was very happy with the performance of her side today.
"The three spinners we have here have been around the squad for a couple of years and all know their roles well and I couldn't have asked for anything more from those girls today.
"We probably had a few things in the field to improve on, we need to get used to the field as was a bit bumpy at times but our batting was great and we need to take that into the match against Pakistan and England," she said.
Australia's next match is against Pakistan on Saturday in Galle.