Mayank Agarwal will make his Test debut and is expected to open the batting with Hanuma Vihari. Rohit Sharma will resume his place in the side after missing the Perth Test through injury.
Vijay and Rahul have scored just 95 runs between them in eight innings across the opening two Tests in Adelaide and Perth.
"As a team, whether you're 2-0 up or 1-0 down, what has happened in the past has no significance to what is going to happen in the next Test," said India skipper Virat Kohli on the eve of the match.
"So the key is to stay in the moment and stay in the present. We just need to play consistently good cricket and not get too excited or taken aback from situations in the match."
Despite winning to level the series in Perth, Australia opted for change by recalling all-rounder Mitch Marsh at the expense of the underperforming batsman Peter Handscomb. The 27-year-old has scored 68 runs in four innings during the first two Tests.
Tim Paine, the Australia skipper, said: "I'm sure Pete will be disappointed but we believe Mitch can come in and do a really good job with the bat and obviously he'll give great support to our bowlers."