India trailed 0-1 at half-time.
India's other goal-scorers were Ritu Rani (45th minute) and Monika Badran (53rd).
Australia got their goals through Casey Eastham (31st minute) and Marnie Hudson (60th).
The Aussies, who finished fourth compared to India's 11th in the last edition of the tournament four years ago, earned 10 penalty-corners but could score only once from them.
India goalkeeper Jasdeep Kaur thwarted the first four attempts but was finally beaten by a direct set-piece by Eastham.
Australia started off the second half with quick passes but lost speed when India carried the ball down the field and Poonam Rani smoothly scored in the 45th minute to draw level.
India kept the momentum going and forged ahead eight minutes later when Monika Badran, set up by Joydeep Kaur, pushed the ball past Australia custodian Ashley Wells.
Stung by the setbacks, Australia intensified their onslaughts and equalised in the 60th minute when Hudson fired home.
India earned their fourth and final penalty-corner when Rani Devi was obstructed in the circle in the 70th minute. Monorama Devi scored from an indirect set-piece to clinch the issue.
India plays Belarus next on Wednesday.
In the day's other matches, Germany [ Images ] beat Argentina 2-1, Korea beat Chile 6-1, South Africa [ Images ] beat Lithuania 3-2, England [ Images ] beat France [ Images ] 5-0, New Zealand [ Images ] beat Netherlands 3-1 and China beat Spain 3-0.