The Australians will thank the weather gods for some respite as poor light and rain forced the umpires to take the players off the field before calling it a day around an hour before the scheduled close of play.
After a somewhat quiet opening session, the Indians took the upper hand after lunch as the Australians lost wickets at regular intervals.
Kuldeep Yadav was the most successful bowler for India with figures of 3/71.
Fellow Left-arm spinner Ravindra Jadeja also took two wickets.
Resuming the day at the overnight score of 24/0, Australia lost their first wicket when Usman Khawaja was dismissed by Yadav.
Khawaja, who was batting slowly and steadily, scored 27 runs off 71 balls with three hits to the fence.
He gave good support to fellow opener Marcus Harris who was in good form at the other end.
Harris was the first to depart after lunch when he was bowled by Jadeja.
Harris scored 79 runs with eight boundaries studding his 120-ball stay in the middle.
Jadeja bagged his second wicket soon after when he sent Shaun Marsh back to the pavilion.
Marnus Labuschagne seemed to be in good touch before Ajinkya Rahane pulled off an excellent catch off Mohammed Shami's bowling.
Travis Head fell to a superb caught and bowled effort by Yadav shortly before tea as the hosts plunged into further trouble.
The Australians ran into even deeper trouble in the very first over after tea as Tim Paine was bowled by a flights delivery by Yadav.
But Cummins and Handscomb ensured that the Australians lost no more wickets before the close of play.
Australia (first innings): 198/5 (Marcus Harris 79; Kuldeep Yadav 2/50, Ravindra Jadeja 2/51) vs India (first innings): 622/7 declared at tea on Day 3.