The Indians lost their last seven wickets for the addition of just 70 runs on the final day of the contest.
Labuschagne has regained the No. 1 position after Root overtook him in mid-June with successive centuries against New Zealand.
The 31-run victory in Adelaide was India's first series-opening win on Australian soil.
Australia racked up 469 in their first innings and then reduced India to 151/5 to put themselves in the box seat in the World Test Championship final.
Batsman Daniel Hughes, returning from an ankle injury but still visibly restricted, top-scored with 42 before being run-out by Marsh, triggering a collapse which resulted in the side being bowled out for 92.
Australia pick two uncapped players for first two Tests
Despite being left with just 75 runs to defend, Umesh Yadav remained positive at the end of Day 2 of the third test between India and Australia in Indore.
Australia can take the top Test ranking from India with a series victory
Images from Day 2 in the fifth Test between Australia and England, in Hobart, on Saturday.
Tendulkar, who had earlier voiced his concern about tackling the dew factor, said the Indian cricket think-tank should do a postmortem after the match gets over.
Cheteshwar Pujara and Ajinkya Rahane shared an unbroken fifth-wicket stand of 93 to keep alive India's hopes of a series-levelling win over Australia, giving the hosts a lead of 126 on a see-saw third day of the second Test in Bengaluru on Monday.
Top order batsman Shaun Marsh was called into the Australia squad for the third Test against New Zealand on Wednesday along with pace bowler James Pattinson and left arm spinner Steve O'Keefe.
Shami ended with a four-wicket haul to help India limit Australia to 263
England crumbled meekly to 107 for eight in reply to Australia's 481 to put the touring side firmly on course for victory in the final Ashes Test after a dramatic second day at The Oval on Friday.
Australia named five uncapped players in a raw tour squad to play Pakistan in a Test series in the United Arab Emirates, while recalling pace veteran Peter Siddle for the first time in two years and dropping middle order batsman Peter Handscomb.
Photos from Day 3 of the first Test played at The Gabba on Saturday
It would be interesting to see who India leave out to play Rohit Sharma
Sent in to bat on a grassy MCG pitch on Sunday, England were skittled for 185
Rohit also said he had picked up a few cues about how to work with spinners from his predecessor Virat Kohli
All-rounder Hilton Cartwright will make his debut for Australia in the dead rubber third Test against Pakistan in Sydney on Tuesday, with left-armer Steve O'Keefe returning to the side as a second spinner alongside Nathan Lyon.
Ravichandran Ashwin will become only the 14th Indian player and 77th overall in world cricket to complete the milestone of 100 Test matches.
England ripped out the last three Australia wickets for 12 runs to win the fourth test by a crushing innings and 78 runs at Trent Bridge on Saturday and regain the Ashes.
Team India began their preparation for the Border-Gavaskar Trophy
Factbox World Cup match between Australia and England at the MCG.
'I'm in the team to take wickets and I've had two wicketless games, so we'll see how we go.'
Promoted to No. 5, Pant played aggressively from the outset, and held his nerve to hit the winning runs as India reached 329 for 7. His knock included nine fours and a six as he stuck to his natural game in the high-pressure closing stages.
Jasprit Bumrah's appointment as India's stand-in Test captain is a 'courageous decision' based on his 'tactical nous', and his leadership duel with England skipper Ben Stokes is providing a fascinating sidelight to an entertaining game in Birmingham, said the legendary Ian Chappell.
Cheteshwar Pujara stood firm to guide India to 151 for three at stumps on Day 3 for an overall lead of 166 runs.
Ashwin responded to Prithi's tweet by saying that it brought him to tears and thanked her for being there with him.
Opener David Warner is still looking for his first Test hundred against Sri Lanka while Smith has managed only one century in his last 18 Tests.
Jofra Archer's first five-wicket haul in Test cricket put England in command on a weather-affected opening day of the third Ashes Test at Headingley on Thursday as they bowled Australia out for 179.
With the second Test set to start on Wednesday, here is a quick fact check on how both teams stand at the Gabba.
Australia were all out for 263 on Day 1 of the second Test at the Arun Jaitley stadium in Delhi, February 17, 2023.
Australia repelled a brief England fightback led by Alastair Cook and Ben Stokes to remain firmly in control of the second Ashes Test on the third day at Lord's on Saturday.
A burgeoning third wicket stand between Babar Azam and Abdullah Shafique had kept Pakistan in the contest and the duo continued to frustrate Australia when play resumed.
South Africa fast bowler Kagiso Rabada will have his appeal against a two-match suspension on Monday as he seeks to play in the rest of the Test series against Australia.
Australia declared their first innings on 556 for nine and then skittled out Pakistan for 148 to seize control of the second Test in Karachi on Monday.
Australia will start favourites in Thursday's clash but a passionate Bangladesh are expected to make life tough for the holders.
On a Karachi track that is expected to break up early, Steve Smith and David Warner created rough patches before facing bowlers in the nets to prepare for Pakistan's full-strength attack.
Pakistan, who briefly topped the Test rankings last year, have now lost six straight Tests, one to West Indies in Sharjah, two in New Zealand and three in Australia.
