Batsman Cheteshwar Pujara hit an unbeaten half-century to lead India's spirited fightback against Australia on the third day of a gripping second Test in Bangalore on Monday, the other highlight being Virat Kohli's dismissal in controversial circumstances.

The hosts were 213 for four at stumps, leading Australia by 126 runs in their second innings after the tourists' hopes of building a big lead were undermined by an oustanding bowling performance by Ravindra Jadeja.

Pujara on 79 and Ajinkya Rahane on 40 were batting at close of play.

The duo put together a stubborn 93-run partnership for the fifth wicket to lift India from a wobbly 120-4 at Bangalore's M Chinnaswamy Stadium.

Virat Kohli was given out in controversial circumstances. PTI

Pujara led the way with his controlled knock as he kept a persistent Australian attack at bay, prompting skipper Steve Smith to rotate his bowling options.

Rahane was equally persistent in his resolve to give the visitors a daunting fourth innings chase as he hardly played a loose shot during his 105-ball stay.

The 29-year-old Pujara, who recorded his 14th Test fifty in his 46th Test, capitalised on a dropped chance by Smith at first slip off Nathan Lyon when he was on four.

Off-spinner Lyon, who had grabbed a career-best Test haul of 8-50 in the first innings, went wicketless on a day when Indian spinner Jadeja claimed six wickets.

It was Australian seamer Josh Hazlewood who rattled the Indian top-order with his three wickets, including the prized scalp of skipper Virat Kohli in the afternoon session.

Pujara is just 21 runs short of a century. Reuters

Hazlewood trapped Kohli lbw for 15 on a shooting inswinger and a review did not help the star batsman as he walked back to a stunned silence at Bangalore's M Chinnaswamy Stadium.

India's move to promote all-rounder Jadeja in the batting order also backfired when the left-hander was bowled by Hazlewood for two to leave the hosts reeling at tea.

India's trouble started when opener Lokesh Rahul fell to left-arm spinner Steve O'Keefe after hitting a dominant 51 and handing India a good start.

Rahul, who top-scored with 90 in India's first innings, put on 45 with Pujara after Abhinav Mukund (16) was bowled by Hazlewood early in the lunch session.

O'Keefe lured Rahul into a drive outside off stump and a diving Smith took a brilliant one-handed catch at first slip.

In the morning session, left-arm spinner Jadeja returned with figures of 6-63 to help dismiss Australia for 276 in their first innings, a lead of 87.

Australia lead the four-match series 1-0 after humbling the hosts in the first match in Pune.

Feature image source: PTI