Akshar and Ashwin forged a 114-run stand to take India's first innings total to 262 in Delhi.
Opting to bat first, Australia posted 263/10 in their first innings on the back of half-centuries from Usman Khawaja (81) and Peter Handscomb (72*).
In reply, the hosts were reeling at 139/7 before spin all-rounders Akshar Patel (74) and R Ashwin (37) forged a 114-run partnership to take the team’s total to 262.
After the second day’s play, Australia off-spinner Nathan Lyon praised Akshar and Ashwin for their batting efforts.
"They are not lower-order (batters). Let's get that clear. Akshar and Ash could easily bat in the top-six in a few teams in Test cricket around the world in my eyes. They (India) have a very long top order, let's just say that," said Lyon.
In their second innings, the visitors batted aggressively to finish the day on 61/1, stretching their overall lead to 62 runs. Travis Head and Marnus Labuschagne were unbeaten in the middle on 39 and 16, respectively.
Nathan Lyon said he will not get into any target setting at the moment.
"I'm not going to give you a number. Whatever we get we have to make sure it's enough. That's the mentality we need to do (go with); we need to come here tomorrow and be really brave."
Lyon, who picked a five-wicket haul in India’s first innings, also backed Travis Head’s aggressive batting in the second dig.
"We need to trust the guys' methods when they have the support of the whole change room to go out there and play the way they want to play and the way they think they can combat the quality bowling India have. Whatever we set, we have just got to make sure it's enough."
Lyon said the more bounce he could extract from the Ferozeshah Kotla track had helped him immensely.
"There is (a) lot more bounce in Delhi compared to Nagpur, which I obviously like to exploit."
"Bowling around the wicket in this game, I'm still trying to target off stump. That's my goal. If you understand cricket, you will understand what I am trying to do and trying to get them defending because we know how good the Indian batters are. If I can make them defend, hopefully, I'll create a few chances here and there."
(With PTI Inputs)