Smith’s 117 not out is only the second century of the spin-dominated series — following his 109 in the first test in Pune — as the 27-year-old joined the 5000-run club in his 53rd test.
Glenn Maxwell celebrated his return to test cricket with a career-best 82 not out, his burgeoning partnership with Smith already worth 159 runs.
Home captain Virat Kohli injured his shoulder while diving to save a boundary in the 40th over and missed the rest of the day’s play.
Earlier, Smith won an important toss and had little hesitation in batting first, something of a ritual on India’s low-bounce tracks, and Matt Renshaw led their brisk scoring with his boundary binge.
With an extremely fast outfield at the Jharkhand State Cricket Association (JSCA) Stadium hosting its first test match, Renshaw’s first 24 runs came all via boundaries as the tourists cruised to the 50-run mark in the 10th over.
Left-arm spinner Ravindra Jadeja got the breakthrough in his first over when David Warner slapped a juicy full toss back to the bowler to depart for 19.
Renshaw looked good for his third fifty in the series before edging Umesh Yadav in the slip having played and survived an identical shot on the previous delivery. Renshaw’s fluent 44 included seven elegant boundaries.
Australia were reeling at 89 for three when Smith and Peter Handscomb (19), protagonists of the review controversy in Bengaluru, joined forces for a half-century stand.
Handscomb had advised Smith to gesture towards the dressing room in Bengaluru for advice on whether to review a leg before wicket decision, a move that drew explosive response from Kohli resulting in considerable acrimony in the four-test series.
Yadav trapped Handscomb (19) lbw with an inswinging yorker but Smith found an able partner in Maxwell, who shunned his natural aggression, and played judiciously to justify his selection replacing the injured Mitchell Marsh.
Known for his destructive batting which makes him a limited-overs asset, Maxwell showed tremendous self-restraint, taking 57 deliveries to hit his first boundary.
There were glimpses of his natural aggression as well, like when he hit Jadeja for the first of his two sixes to bring up his maiden test half-century.
Maxwell surpassed in his very first innings of the series the 48 runs that Mitchell Marsh had totalled in his four during the first two tests and the all-rounder is not done yet.
Australia also brought in paceman Pat Cummins, who is playing his second test after more than five years in the wilderness, to replace the injured Mitchell Starc.