Australia tightened their grip on the pink ball Test as their formidable pacers scythed through India's top-order after nemesis Travis Head's counterattacking century handed his team a substantial first-innings lead on a riveting second day here on Saturday.

The Adelaide Oval was throbbing with life through the three sessions of play as Head dominated India with his wide range of strokes on way to a 140 off 141 balls before the trio of Scott Boland (2/39), Mitchell Starc (1/49) and Pat Cummins (2/33) left the visitors in a spot of bother at 128 for five in their second innings and trailing by 29 runs.

At stumps, Rishabh Pant was living dangerously on a 25-ball 28 and Nitish Reddy was batting on 15 off 14.

Thanks to Head's eighth Test century, which he reached in 111 balls after toying with the Indian bowling attack, Australia ended with 337 all out, and more importantly, a 157-run first-innings lead.

The hosts are looking to restore parity in the five-match series after the 295-run hammering in the opener at Perth.

Head's hundred, the fastest in a pink ball Test, reduced Marnus Labuschagne's (64) composed half-century, coming after a lean run of form, to a mere footnote.

India lost KL Rahul (7) early in their second innings and Yashasvi Jaiswal (24) was done in by a peach of a delivery from Boland, who again struck with his first delivery that had a hint of late movement.

Boland then had Virat Kohli (11) caught behind after he got one to land right in the channel which has been troubling the Indian batting mainstay for a while now.

To make matters worse for the visitors, Starc knocked down Shubman Gill's (28) middle stump with his late in-swing doing the damage to leave India at 86 for four in front of a record crowd of over 50,000.

However, unperturbed by the Australian inroads, Pant looked to be batting in a universe of his own and played some outrageous shots against the fast bowlers, leaving everyone stunned.

Least bothered by the fact that India were three down with not enough on the board, Pant danced down the track first ball and smashed Boland over mid-off for a boundary, and he maintained that audacious approach until the umpires called stumps.

Earlier, Head continued to be a thorn in India's flesh with yet another magnificent knock that powered Australia's response after bowling out India for 180.

Head, who got off the mark with a cracking boundary off Jasprit Bumrah (4/61), got a reprieve on 76 as Mohammed Siraj failed to complete the catch despite getting both hands to it after the batter tried to slog-sweep R Ashwin, having just smashed his third six against the off-spinner.

Amid the rejoicing around Head's century, Siraj (4/98) was rewarded for his discipline as he had Alex Carey caught (15) behind following a faint outside edge with Australia's lead crossing 100.

Desperate to prevent Australia from adding to that advantage, India took the second new ball the moment it was made available to them, and their lead pacer Bumrah too was brought back into the attack.

Bumrah, however, pulled his adductor muscle as the physio attended to him. Fortunately for India, Bumrah was up on his feet quickly and ready to bowl again, even as Head flicked him for two boundaries in between.

During his knock, Head played some incredible shots, including a pick-up six over Siraj over deep square leg, but the pacer had the last laugh as he brought his innings to an end when he cleaned him up with a yorker.

In all, Head struck 17 fours and four sixes.

Earlier, Rohit Sharma giving his strike bowler Bumrah only four overs in the first session seemed odd, and so were some of his field placements.

Then, in another surprising move, he started the proceedings after tea with Ashwin instead of the fast bowlers.

Luck, though, was with Ashwin as Mitchell Marsh decided to walk off despite a half-baked appeal by the Indian team.

Seeing Marsh heading in the direction of the dressing room, Richard Illingworth raised his finger too, but replays clearly showed there was a gap between bat and pad.

Head, though, went about his task in the manner he does best -- dictating the terms to the bowlers with his free-flowing strokes.

None of the Indian bowlers, including Bumrah, looked like they could cause problems for Head.

Except for the headline, this story has not been edited by The Telegraph Online staff and has been published from a syndicated feed.