At the break on day four, Australia were 104-5 with a defiant Travis Head not out 63 and Mitchell Marsh on five as they chase a near insurmountable 534 to win.
The 22-year-old resumed on day three 10 runs shy of his fourth Test ton and reached three figures off 205 balls with a six off Josh Hazlewood
India have won their last two Border-Gavaskar trophy series in Australia, but began this campaign after a demoralising 3-0 home defeat to New Zealand.
India head into the first of five Tests against Australia on Friday in Perth on the back of their first home series loss in 12 years.
India won 2-1 against Australia on both of their last two Test tours, but suffered a 3-0 whitewash at home to New Zealand last month.
“Honestly, if they really needed myself for this series, I’m more than happy to play the next Shield game and go out there and play (the first Test)," Warner said.
Smith has been a rock in Australia's middle-order for more than a decade, but was moved up to an unfamiliar role at the top alongside Usman Khawaja with mixed success when fellow veteran David Warner retired from Test cricket at the start of the year.
The hosts won the series 2-1 and the world's two top-ranked teams will do battle again on June 7-11 at The Oval in the World Test Championship final
India also confirmed their place in the World Test Championship final against Australia in June following Sri Lanka's two-wicket loss to New Zealand in Christchurch earlier in the day
Smith led Australia between 2014 and 2018 before he was stripped off the honour following a ball-tampering scandal in South Africa
A winning target of 76 may sound a cakewalk but Australia will have to score those runs on a track where 30 wickets have tumbled on the first two days of the spin-dominated contest.
Milking 'home advantage' is commonplace in international cricket and India have never shied away from preparing pitches that would suit their spinners
The tourists were 156-4 at stumps after Usman Khawaja hit a gritty 60 to drive his team's reply on a viciously turning pitch in Indore
Ashwin and Jadeja destroyed Australia's batting to set up a six-wicket victory in Delhi on Sunday and give India an unassailable 2-0 lead in the four-Test series
Captain Pat Cummins will also be returning to Australia due to a serious family illness but will be back in time for the third Test starting in Indore on March 1
Australia are 2-0 down in the four-Test series after being thrashed by six wickets in the second match in Delhi on Sunday
The tourists, who suffered a heavy defeat in the opening Test and were dismissed for 263 in their first innings on Friday, will bring Matt Renshaw into the team as a concussion substitute, the reports said
The left-handed Warner scored one and 10 at Nagpur last week and has struggled for form since scoring 200 in the Boxing Day Test against South Africa in Melbourne.
The 35-year-old will be the 13th Indian cricketer to play a century of Tests when he takes to the field against Australia in New Delhi.