Australia were all-out for 285 in their second innings as their overall lead swelled to a gigantic 440 runs courtesy Smith's 18th Test hundred.
The Australian skipper scored 109 off 202 balls with 11 boundaries, an innings that will certainly be considered as one of the best by an overseas batsman on a devilish Indian track which had sharp turn and bounce. It was his fifth consecutive century against India in as many Tests.
Australia today added 142 runs in the extended opening session in 41 overs after commencing at the overnight score of 143 for 4 with Smith (59) and Mitchell Marsh (21) at the crease.
Smith curbed his natural attacking instincts to slowly and steadily using his feet to good effect.
However, by the time of the visiting team's skipper departure at 246 the Australian lead had gone well past the 400 mark - a huge one by any reckoning that looks impregnable on this treacherous pitch.
Jadeja sent back Marsh for 31 and Stephen O'Keefe for 6 to terminate the innings and end up with innings figures of 3 for 65 while Ashwin's analysis read 4 for 119.
Umesh Yadav, the only other successful bowler, finished with 2 for 39 to add to his 4 for 32 in the first innings.
He looked unflappable even after being reprieved on quite a few occasions before reaching the 18th hundred of his career, and fifth against India, by striking a four and then taking a couple of runs off Ravindra Jadeja in the left-arm tweaker's second spell of the day.
Smith's superb effort has effectively shut the door on the Indians in their pursuit of taking a 1-0 lead in the four-game rubber.
The butter-fingered Indian fielders, who dropped Smith on 27 and 37 yesterday, continued to grass him as Ajinkya Rahane failed to latch on to a sharp chance at leg slip when he had added 7 runs to his overnight total.
On 73, Smith again got a lucky break when umpire Richard Kettleborough of England ruled him not out when he was trapped right in front of the stumps by Ravindra Jadeja, to the chagrin of the hosts who had frittered away both their reviews at this stage.
This was soon after Jadeja had struck the first blow of the morning when he removed the other overnight not out batsman Mitchell Marsh who edged him to Wridhiman Saha behind the stumps after making 31 in 76 balls.
In fact Marsh was the more aggressive of the two overnight batsmen as he struck Ashwin for three fours when the off spinner erred in line.
A double change was introduced by captain Virat Kohli in bowling with Ashwin, after a wicket less spell of 6 overs for 23 runs, giving way to Jayant Yadav and Umesh Yadav, who was the pick of the bowlers with a four-wicket haul in the first essay, replacing Jadeja after the bowler's tight and successful spell of 7-2-12-1.
Yadav broke the sixth wicket stand between Smith, crawling closer to his first century in India and fifth against the same opposition, and wicket keeper Matthew Wade through a catch at the wicket dismissal.
Wade's dismissal left the visitors on 204 for 6 for an overall lead of 359, already a formidable sum in Indian conditions and made more so by the state of the track at the Maharashtra Cricket Association Stadium on which 24 wickets had fallen on the first two days.
Smith reached his maiden ton in India in 187 balls to raise his hands in the air in celebration, but was removed by Jadeja when he missed a pull shot and was rapped on the pads. Umpire Nigel Llong raised his finger, Smith reviewed the decision through TV replays which confirmed that the umpire was right in declaring him out.
Umesh Yadav later trapped Nathan Lyon leg before as the session was extended before Jadeja had O'Keefe caught behind and the innings ended signaling lunch.
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