Pat Cummins struck thrice on a tense third day of the third Test to give Australia hope of a victory over India that would ensure the visitors retain the Border-Gavaskar trophy.

The four-Test series is level after two dramatic matches and the contest in Ranchi is on track to be a classic. India were 360-6 at stumps on Saturday, trailing Australia by 91 runs.

Cummins and Josh Hazlewood bent their backs throughout an absorbing day in which wickets and runs were hard to come by. Virat Kohli was out cheaply again, while Cheteshwar Pujara became the top-ranked Test side's first centurion of the series.

Pujara was 130 not out at stumps. Steve Smith will feel aggrieved the talented batsman wasn't dismissed on 22 when a contentious referral was turned down by third umpire Nigel Llong.

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Smith reviewed a confident lbw shout from Steve O'Keefe. Front-on replays appeared to show the ball hit bat before pad, but the Snickometer picked up a clear noise that suggested it might have glanced the pad first.

Llong was interested only in the raw footage.

Cummins continued to excel in his first Test since a memorable debut in 2011.

"Last night he bowled particularly well, but today he backed that up," Australia's bowling coach David Saker said.

"Hats off to the selectors to go with him. Ball speed in India is a big thing because the wickets don't generate any pace.

"He was way higher than the expectations we had."

The injury-prone express paceman started the day with three consecutive maidens and always looked the bowler most capable of creating a breakthrough.

The 23-year-old removed Ajinkya Rahane and Ravichandran Ashwin with bouncers, and he claimed the key scalp of Kohli.

"He was bowling really well and he was sharp in the early spell ... it was a good challenging test for us to battle against him," India opener Murali Vijay said.

Cummins also snared the only Indian wicket to fall on day two, when a short-pitched delivery caught KL Rahul by surprise.

"He deserves a five-for. He's been outstanding in his first Test back," Michael Clarke said on Star Sports.

Kohli continued his miserable series when he attempted to drive the first delivery he faced from Cummins. The resultant edge rocketed to Smith at second slip.

The injured skipper, who sarcastically applauded Smith's failed review in the morning session from the balcony, was out for six. He has totalled just 46 runs from five digs in the series.

"There's a lot of pressure on him," Saker said.

"When you lose your two reviews it's a bit of a relief to the opposition and he probably just showed that.

"It's very satisfying getting Virat Kohli out cheaply.

"We've got the better of him, but we know he's such a good player that he could bounce back at any time."

Vijay insisted it was "a matter of time" before Kohli found form again.

"It'll be sooner than later," Vijay said.

"He's a world-class player and to judge a player on two or three innings is unfair."

- AAP