PIX: Lyon snares Kohli but India in control in Adelaide

Cheteshwar Pujara and Virat Kohli thwarted Australia in a diligent partnership to push India to a position of strength and a 166-run lead at the close of day three of the first Test on Saturday.

Brought together before tea with India vulnerable at 76 for two, the pair stood firm through the best part of a session before spinner Nathan Lyon snared Kohli for 34 to end their 71-run stand at Adelaide Oval.

Pujara, who rescued India's first innings with a sparkling 123, survived to stumps on 40 not out, with number five Ajinkya Rahane on one run under a cloudy sky.

Lyon was denied Pujara's wicket twice by the Decision Review System, so his Kohli breakthrough was a relief after a long afternoon's toil.

Deceiving the Indian talisman with flight and dip, he caught Kohli's inside edge and the nick popped up to Aaron Finch at short leg.

Dismissed for three in India's first innings 250, Kohli was fuming to have his second knock cut short but soaked up 104 balls to frustrate the home crowd, sections of which had jeered him as he strode out to the crease.

He also managed to join an elite club of Indians who have notched 1,000 Test runs in Australia, with only Sachin Tendulkar (1,809), VVS Laxman (1,236), Rahul Dravid (1,166) and Virender Sehwag (1,031) ahead of him.

Having conceded a 15-run lead after being dismissed for 235 before lunch, the home side will be desperate for early wickets on day four to have hope of containing the tourists.

Jasprit Bumrah, who took 3-47 to finish with India's best bowling figures, looked forward to the spin of Ravichandran Ashwin coming into play on a fifth day wicket.

"In the fourth innings he will obviously play a crucial role," said the paceman of Ashwin, who took three first innings wickets and was a constant handful.

"We saw Nathan Lyon using the rough to his advantage so I think (Ashwin) knows what he has to do."

With only 250 to defend, India's bowlers could take great pride in restricting Australia to 235.

With lusty tail-end cameos by Mitchell Starc (15) and Nathan Lyon (24 not out), Australia looked set to race past India's total after resuming on 191 for seven in the rain-delayed morning.

But Mohammed Shami swung the momentum back to India and was on a hat-trick after claiming the final two wickets of batsman Travis Head (72) and number 11 Josh Hazlewood (0).

India's openers put on a 63-run opening stand to press the advantage before Australia fought back to remove them both.

Hazlewood had Lokesh Rahul caught behind for 44 after fellow seamer Starc snared Murali Vijay in the slips for 18, both batsmen again falling to loose shots after soft dismissals in the first innings.

Kohli and Pujara then steered India to safety and a platform to set up a rare test victory Down Under and an early lead in the four-test series.

"It’s just a really big hour in the morning to change that momentum and to get us going," said Head.

"If we can get the wickets in the morning and then put them under pressure with the new ball, anything's gettable."