Iyer, who has been knocking on the doors of the national team over the past couple of seasons with his attacking batting in domestic cricket, could not have chosen a better platform to showcase his talent, smashing 5 sixes and 7 fours in an almost run-a-ball innings to remain unconquered on 85 in a team score of 176 for 4 in 51 overs.
India 'A' were 293 runs in arrears at stumps.
Starting his innings in stunning fashion with a six over long on off the first ball he faced from Nathan Lyon, Iyer dominated the rival bowling, barring Jackson Bird, who was the pick of the Australian bowlers with his pace and movement at the Brabourne Stadium.
Iyer gave just once chance, off Lyon, soon after reaching his half century in 44 balls, but otherwise dominated the Aussie spin duo of Lyon, whom he hit for three sixes, and left-arm spinner Stepen O'Keefe, who was hoisted for two over the ropes by the youngster.
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The 22-year-old batsman's innings was the pick of the India 'A' reply in which opener Priyank Panchal made 36 with six fours in 77 minutes, but was beaten often by lanky pacer Jackson Bird.
The other opener Akhil Herwadkar struggled his way to 4 in 48 minutes, Ankit Bawne made an attractive but all-too-brief 25 in 39 minutes with four hits to the fence while skipper Hardik Pandya too got a start before departing late in the day for 19, caught behind off Bird.
Iyer and Bawne had earlier steadied the innings after the loss of the two openers with a stand of 57 for the third wicket.
For Australia, Lyon - although punished by Iyer - showed good form as he got purchase off the track to pick up 2 for 72 while Bird, easily the most impressive of the visiting team's bowlers, did not allow the batsmen any freedom and also got rid of Pandya to end with excellent figures of 2 for 15 in 11 overs.
In reply, India A made 63 for two wickets with openers Akhil Herwadkar (4) and Priyank Panchal (36) dismissed at the stroke of tea - both falling to off-spinner Nathan Lyon, who is expected to be the main spin bowler in the four-Test series commencing at Pune on February 23.
The unbeaten batsman at the end of the second session was Iyer.
Earlier, Marsh made 75 after a stay of 200 minutes during which he hit one six and 11 fours while the left-handed Wade scored 64 with nine fours in his 161-minute stay before getting out just before lunch against part-time bowler Herwadkar.
Yesterday skipper Steve Smith and Shaun Marsh hit individual hundreds in impressive fashion to be followed. On day two, Mitchell Marsh and wicketkeeper Wade hardly looked in any trouble and the visitors would be pleased with the time spent in the middle by all the batsmen.
Australia declared when Glenn Maxwell and O'Keefe were at the crease with 16 and 8 respectively and in reply, the home team's openers Herwadkar and Panchal faced a testing time against Australia new ball bowlers Bird and Marsh.
One-down Iyer started his innings with a first-ball six over long on off Lyon while Panchal grew in confidence after his early trouble against Bird.
Pujara used his feet well against the spinners and never
allowed them to settle down on a wicket that aided some turn. He was extremely choosy while leaving balls released by pacers Cummins and Hazlewood.
He brought up his fifty with two exquisite boundaries on both sides of the wicket -- a flick of the wrist before stepping out to drive O'Keefe with the turn.
Vijay was solid with his defence, and was not afraid to step out and punish the loose balls. With Pujara at the other end, India progressed with caution.
Having got the solitary wicket of KL Rahul with a rising delivery yesterday, Cummins was introduced in the ninth over of the day and the duo of Pujara and Vijay was happy when the pacer was through with his spell.
Cummins bowled three successive maidens, conceding eight runs from his nine overs before being replaced by Nathan Lyon, as Australia resorted to spin from both ends.
The final Test will be held in Dharamsala from March 25 to 29.