Ashwin accounted for Shaun Marsh (3) and Ed Cowan (30) in two separate spells, while pace spearhead Zaheer Khan dealt the first blow, dismissing David Warner (8) early to give India the edge in the first session.
Veteran Ricky Ponting though was in brilliant touch and has so far hammered seven fours in his 43 off 83 balls. Skipper Michael Clarke was giving him company on 8.
The hosts, 3-0 up in the series, were stuttering at 31 for two by the 10th over at one stage before Cowan and Ponting redeemed the situation somewhat with a 53-run stand.
Zaheer, as is his wont, gave India the first breakthrough after Australia chose to bat in hot, batter-friendly conditions at the Adelaide Oval here.
Warner (8) played back to a Zaheer delivery and was struck plumb in front of the stumps in the seventh over of the innings.
Off-spinner Ashwin, introduced into the attack as early as in the fourth over, sent down a delivery which went through the arm and clipped the top of Marsh`s off-stump.
However, once these two bowlers were through their first spells, Indians leaked runs all around with Umesh Yadav conceding as many as 41 runs from his five overs.
Ponting took a heavy toll of Yadav and struck him all around the park, pulling and hooking with disdain and driving through the off-side with pinpoint precision. There were flicks and unintended steers too for boundaries from the middle order batsman.
Australia were 44 for two after 15 overs in the first hour and the 50 of the innings was up in the 18th over when Ponting flicked Yadav off his pads to fine leg boundary. Ashwin was re-introduced in the half hour before lunch and Ponting decided to take him on by sweeping him in front of square leg for a four.
The off-spinner though made it a sweet session for himself when Cowan drove him straight to short midwicket where VVS Laxman took a brilliant low catch to his right.
Clarke, almost as soon as he arrived, hit Ashwin gloriously through extra cover for his first boundary.