Australia's Travis Head has been a perennial thorn in India's flesh and it was more of the same on Saturday as the left-hander produced a match-defining hundred to deflate the tourists in the day-night second Test in Adelaide.

Head produced match-winning hundreds on both occasions when Australia beat India in the finals of the World Test Championship and the 50-overs World Cup last year.

The 30-year-old reprised the India tormentor's role at the Adelaide Oval where he wowed 51,642 fans with a breakneck 140 that put Australia on the verge of a series-levelling victory.

"It was a tough wicket to bat on and at certain stages, they bowled really well," the middle order batter said after the second day's play.

"Nice to take my luck where I got it and put the guys in a really good position fast-forwarding the score.

"At the moment, the game's got moving pretty quickly, but feels like we're in a great position."

Head got two reprieves in his entertaining knock - Mohammed Siraj spilled a tough chance in the deep and one of his edges flew between the wicketkeeper and the fielder at first slip.

The feisty southpaw particularly targeted Ravichandran Ashwin, hitting India's premier off-spinner for three sixes in what he later called a calculated move.

"When they've got the quality of quicks that they've got, I guess you've got to target something," Head said of his approach.

"I felt like I navigated through his spells really, really well, and was able to get the quicks back at certain stages into that new ball."

Head took a single off Ashwin to bring up his hundred at his home ground and gestured to his wife, daughter Milla and newborn son Harrison in the stands.

"I did it when Milla was born so I would have got a bit of stick from the missus if I didn't do that when Harrison was born," Head said of his rock-the-baby celebration.