Australia skipper Steve Smith continued to defy India with a masterful innings in Ranchi, but the hosts produced a solid response with the bat on the second day to leave the third Test intriguingly poised.
Smith advanced from his overnight score of 117 to finish unbeaten on 178, the fifth-highest score by a visiting captain in India, while Glenn Maxwell completed a maiden Test hundred as Australia posted 451 all out in their first innings, Ravindra Jadeja returning 5-124.
Yet on a pitch offering far less assistance to the bowlers than many had anticipated, India were able to reach 120-1 in reply, KL Rahul leading the way with 67.
It remains unclear whether India captain Virat Kohi will come in next after injuring his shoulder in the field on day one.
Rahul fell late on day two to Pat Cummins - a notable moment for the injury-plagued Australia quick on his return to the Test arena.
Cummins starred on debut against South Africa as a teenager in 2011, but went more than five years without a first-class appearance prior to a Sheffield Shield outing for New South Wales earlier this month. His fitness may well be tested over the coming days given the apparently docile nature of the Ranchi wicket.
Australia, who were beaten in Bangalore last time out to leave the four-match series tied at 1-1, resumed on 299-4, with Maxwell 18 runs short of a first century in the five-day format.
After a bizarre start to proceedings, which saw Maxwell's bat break as he defended the first ball of the day from Umesh Yadav, the all-rounder reached three figures with a cut four off Yadav.
However, he soon fell to Jadeja for 104 as the spinner completed a fourth maiden in succession.
And although Smith continued to hold firm, Jadeja had further reason to celebrate prior to lunch as he ousted Matthew Wade (37) and Cummins in the same over - the latter cleaned up by a wonderful delivery.
Smith shared 51 with Steve O'Keefe before the last three wickets fell in a hurry. O'Keefe was caught at fine-leg off Yadav, while Jadeja had Nathan Lyon caught at silly point and then ran out Josh Hazlewood to leave the visiting captain stranded.
There were few alarms for India in reply, but Cummins (1-22 from 10 overs) produced a fine delivery to account for the fluent Rahul, a well-directed bouncer taking the glove through to wicketkeeper Wade.
Murali Vijay (42 not out) and Cheteshwar Pujara (10 not out) saw out the remaining overs, the former surviving an optimistic review for a bat-pad catch off Lyon in the penultimate over.