Australia started their chase nervously and almost lost opener Aaron Finch in the first over. Ishant Sharma trapped him leg before wicket but the opener decided to review and replays showed Ishant had overstepped.
However, Ashwin struck at the stroke of tea, getting Finch caught behind for 11, though the snicko and hotspot showed no signs of any nick. Finch opted not to review.
His partner, debutant Marcus Harris, didn't last long either, edging one from Mohammad Shami to Rishabh Pant for 26.
Ashwin then accounted for Khawaja (8) - who played a poor shot, holing out to deep extra cover where Rohit Sharma completed a fine catch - and when Shami removed Handscomb (14), it seemed India would scythe through the Australian middle-order. However, Shaun Marsh showed some fight for the hosts along support from the star of first innings Travis Head and carried them safely to stumps without further dents.
Earlier, Cheteshwar Pujara and Ajinkya Rahane slammed valuable half-centuries as India set Australia a daunting target.
Play started 30 minutes early to make up for rain disruptions on Saturday, and India started the day on 151 for 3. Australia were desperate for an early breakthrough but Rahane and Pujara tackled the Australian attack expertly, scoring quickly to extend India's lead.
Pujara brought up his 20th half-century with a three off Lyon and hardly looked untroubled until he was snared by Lyon half an hour before lunch. At the other end, vice-captain Rahane was also solid, surviving a review for a bat-pad catch off Lyon. He made the most of the reprieve by smacking the next ball for four and brought up his 16th half-century with another boundary.
Rohit Sharma was the only failure with the bat, out for one with Peter Handscomb taking a good catch at silly point, again off Lyon. Rishabh Pant came out all guns blazing and targetted Lyon, hitting him for 18 runs in one over with three boundaries and a six right after lunch to give the Indian innings momentum.
The wily spinner though had the last laugh, dismissing Pant for a quickfire 28 off 16. Rahane became Lyon's next victim as he looked to up the ante, dismissed for 70.
The Indian lower-order folded up quickly, with Mohammad Shami and Ishant Sharma being dismissed for ducks. Starc ending with figures of 3/40 and helping clean up the tail.
India will start the final morning aware that they hold the edge though Marsh can take some inspiration from his heroics last month at the same venue when he scored an unbeaten 163 to help Western Australia get past 313 to beat South Australia in a Sheffield Shield game.
The highest successful fourth innings Test run chase at Adelaide in modern times was 239 in 1982, when the West Indies managed the feat. The only chase of 300 plus was achieved in 1902.
Ajinkya RahaneAustralian cricket teamCheteshwar PujaraIndia vs AustraliaIndia vs Australia 2018Indian cricket teamjasprit bumrahmohammad shamiRavichandran Ashwin
First Published: December 9, 2018, 1:26 PM IST