Cheteshwar Pujara again frustrated a toiling Australia bowling attack as India built a healthy lead on day three of the first Test in Adelaide.

First-innings centurion Pujara patiently compiled an unbeaten 40 from 127 balls to help his side, who had earlier secured a first-innings advantage of 15, reach stumps 166 ahead on 151-3.

The number three was twice given out off Nathan Lyon deliveries yet overturned both decisions using DRS on a rain-affected day that saw the honours go to the tourists.

Lyon did claim the key wicket of India skipper Virat Kohli (34) late in the evening session, but Australia look set to face a stiff target on a pitch that has so far proved difficult to score on.

After rain halted the start of play by almost an hour, India wasted little time claiming the three wickets required to end the first innings of Australia, who resumed on 191-7.

Mitchell Starc was the first to go as he edged behind to wicketkeeper Rishabh Pant after being tempted into a big drive by Jasprit Bumrah (3-47).

Travis Head (72) and Lyon (24 not out) claimed some valuable runs, chipping away at India's lead, but the former and Josh Hazlewood (0) fell victim to Mohammed Shami (2-58) in consecutive deliveries, ensuring Australia were dismissed for 235.

After claiming his first Test half-century in Australia, Head was caught behind from a beautiful Shami ball and Hazlewood immediately followed in similar fashion as India wrapped up the innings.

The covers were back on just as India stepped out to begin their second dig and, once the weather cleared, the tourists made a slow and cautious start.

Negotiating the new ball, India only scored 11 runs from nine overs but the run rate soon rose as KL Rahul and Murali Vijay settled at the crease.

Australia did have some success thanks to Starc, who claimed the wicket of Vijay (18) for the second time in the match when the opener edged to Peter Handscomb in the cordon, India reduced to 63-1.

Either side of tea, Lyon twice thought he had Pujara, only to see decisions for caught behind and lbw overturned.

India's first successful review was followed by a needless dismissal in the next over as Rahul tried to loft Hazlewood over mid-off and instead edged through to Tim Paine.

Pujara and Kohli then regained the initiative for India with a third-wicket stand of 71, but that alliance was broken shortly before stumps when the captain was caught at short-leg off Lyon. Australia's off-spinner has now taken Kohli's wicket more than any other bowler in Tests.