The hosts, resuming on 24-0, played patiently in the morning session, with opener Marcus Harris making 79.
However, Harris was dismissed two balls after lunch before all-rounder Marnus Labuschagne fell to a stunning catch by Ajinkya Rahane at mid-wicket.
Bad light ended play early with Australia 236-6, trailing by 386 runs.
India, who lead the series 2-1, are searching for their first Test series victory in Australia since they began touring in 1947-48.
Australia reached 122-1 at lunch after Usman Khawaja was dismissed by wrist-spinner Kuldeep Yadav, but the rest of the top order could not build on the start.
Veteran Shaun Marsh edged left-arm spinner Ravindra Jadeja to slip for just eight before Travis Head was caught and bowled by Yadav.
Captain Tim Paine then fell quickly after tea, bowled by Yadav for five, but Peter Handscomb and bowler Pat Cummins offered some resistance before the light intervened, with the Aussies still needing 187 more to avoid the follow-on.