Australia started off the second half with quick passes but were slowly losing out on speed to the Indians and Rani fired the equaliser with a fine field goal in the 45th minute.
India kept the momentum going and broke the deadlock when Monika was brilliantly set up by Joydeep Kaur and she pushed her shot past custodian Ashley Wells.
Trailing 2-1, Australia intensified their attack and drew level 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 and Monorama fired in the winner. India will play Belarus next.