Usman Khawaja’s 180 and a maiden Test century from Cameron Green helped Australia take control against India on the second day of the fourth Test.
Khawaja and Green shared a 208-run stand, with Green making 114 as Australia posted an impressive 480.
Off-spinner Ravichandran Ashwin finished with 6-91 as India eventually bowled out the visitors in Ahmedabad.
Openers Rohit Sharma and Shubman Gill saw out 10 overs as India closed the day on 36-0, trailing by 444 runs.
Australia are seeking victory in order to draw the series 2-2.
Regular Test captain Cummins had returned to Australia before the third Test, with Steve Smith acting as stand-in skipper.
Khawaja spent 10 hours in total at the crease, building on his opening day 104 to put Australia in a dominant position.
Green, who missed out on selection for the first two Tests, provided solid company for Khawaja, hitting 18 fours in his 170-ball innings.
Khawaja’s stand was eventually ended by left-arm spinner Axar Patel, while all-rounder Green was caught down the leg side off Ashwin.
“It’s a very good wicket, so I think you’ve got to maybe swallow your ego a bit,” Green said.
“I think tomorrow probably it just will be a holding role for myself and let the spinners get to work.”
Should Australia draw the series, they would become the first side to avoid defeat in an away Test series against India since England won on their tour of 2012.
Victory for India would guarantee their place in the World Test Championship final in June.