Play was officially called after a 17th rain delay forced players from the field for a final time on Wednesday, leaving the series drawn at 1-1 with two to play.
A result always looked near-impossible after India avoided the follow-on on Tuesday night and were bowled out for 260 early on day five.
But after about two hours were lost to rain, Australia slumped to 7-89 in a chaotic 18-over cameo before declaring and setting India 275 to win in the final innings.
That gave Australia 54 overs to bowl India out and claim victory, only for play to be abandoned after 13 balls with India 0-8 as more storms hit the ground just before tea.
The result means India are one win away from retaining the Border-Gavaskar Trophy, given they are the current holders of the prize.
Steve Smith strolled down the pitch to Mohammed Siraj one ball and was gone the next 👀 — cricket.com.au (@cricketcomau) #AUSvIND pic.twitter.com/TPpdBCT9ofDecember 18, 2024
Australia had clearly been attempting to advance the game during their collapse, with almost all wickets falling to attacking shots.
But it made for an ugly scorecard.
Usman Khawaja was bowled by Jasprit Bumrah on eight, while Marnus Labuschagne was caught behind off the quick on one.
Nathan McSweeney played a poor shot to be caught behind cutting Akash Deep on four, while Mitch Marsh also edged off to Akash on two.
After walking out at No.6 Steve Smith was caught behind down legside off Mohammed Siraj on four, as Australia crumbled to 5-33.
Travis Head (17), Alex Carey (20no) and Cummins (22) added some respectability to the board, as the only men to reach double figures.
Mohammed Siraj was among the wicket takers as India crashed through the Aussie top order. (Jono Searle/AAP PHOTOS)
Before Wednesday it appeared Australia would leave the rain-interrupted Gabba Test feeling they were the better team, after claiming a 185-run first-innings lead.
But a day after losing Josh Hazlewood for the rest of the series to a calf complaint, there is now some pressure on the hosts.
Australia's top three are struggling for runs, with Marnus Labuschagne's 64 in Adelaide the only half-century between the trio.
Khawaja's scores in this series now read 8, 4, 13, 9no, 21 and 8, with the opener having gone 11 innings since his last half-century in a Test.
The left-hander turned 38 on Wednesday, and his chances of the dream farewell in next summer's home Ashes series are appearing increasingly uncertain.
Questions also surround McSweeney as an opener, after having never batted there in the Sheffield Shield before his Test debut last month.
The South Australian captain has scored 72 runs at an average of 14.4 in his rookie series, with his fighting knock on night one in Adelaide the highlight.
At the same time, Sam Konstas continues to knock down the door in domestic cricket, with 670 runs at 55.83 in long-form games
Josh Inglis also remains with the Test squad as a back-up batter, after a big start to the summer in the Sheffield Shield.
Travis Head has played down oncerns over a tight quad during Australia's second innings. (Jono Searle/AAP PHOTOS)
Australia's selectors will consider a squad for Melbourne and Sydney on Thursday, but captain Cummins insisted the top order should not be judged too harshly.
"The trend all over the world is the top three is a really hard place to bat at the moment, especially here in Australia," Cummins said.
"There are snippets that have been important. Like the first innings, Travis Head walks in 35 overs into the game (and hits a century), same in Adelaide.
"Obviously we would like them to score more runs, but I think they have made some important contributions that others have benefited from."
Cummins also said he was not concerned the last-day collapse would hurt Australia in the long run.
"I can't say I've ever been scared of momentum. Don't really care about that," he quipped.
"I think we can take lots from this week.
"A couple of great partnerships, to be sent in and score 450 and then being a bowler down and managing to bowl India out for 250."
Cummins' comments came as Australia also downplayed concerns around Travis Head's tight quad, while knowing they will need far more than Mitch Marsh's two overs at the Gabba in Melbourne.
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