Australia still believe they have a "massive sniff" of winning the first Test against India despite a difficult fourth day in Adelaide, according to Nathan Lyon.

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.

 

Cheteshwar Pujara claimed his first century on Australian soil to rescue India from a top-order collapse and leave honours even on day one of the opening Test.

Nathan Lyon will be crucial to Australia's chances of beating India in the upcoming Test series, according to Josh Hazlewood.

Australia left out several senior players for their Twenty20 matches against South Africa and India as Marcus Stoinis and Jason Behrendorff were included in a 13-man squad.

Mitchell Starc, Nathan Lyon, Peter Siddle and Mitchell Marsh were omitted from the squad due to Australia's busy schedule.

Australia coach Justin Langer said the selectors wanted the quartet to focus on the upcoming four-Test series against India.

"We know coming off the back of the tour to the UAE, a huge summer at home, and the World Cup and Ashes just around the corner that we have to get the balance right between playing our best T20 team and preparing for the upcoming Test series," he said.

"While I know all four have a desire to be playing cricket for Australia in every format, with a really tough Test series against India coming up, we believe their best preparation is to go back and get some really good cricket under their belts in the Sheffield Shield."

Australia will play one T20 against South Africa before meeting India in three ahead of their Test series.

Langer was pleased to welcome back Stoinis and Behrendorff, who has taken four wickets at 6.50 in his previous two T20 internationals.

"Marcus missed our recent T20 matches in the UAE because he hadn't resumed bowling, but now he's back to full fitness he'll add great depth to the squad," he said.

"Marcus is such a versatile player, he's a powerful middle-order batsman and he provides us with another solid bowling option.

"Jason Behrendorff has also earned a spot in the squad after returning to full fitness. It was exciting to see him bowl well in the JLT Cup and in the recent Prime Minister's XI match, and it gave us more evidence of how devastating he can be with the new ball. Tactically we believe it's important to have a good left-arm swing bowler at our disposal for the four matches."

 

Australia: Aaron Finch (c), Alex Carey (vc), Ashton Agar, Jason Behrendorff, Nathan Coulter-Nile, Chris Lynn, Glenn Maxwell, Ben McDermott, D'Arcy Short, Billy Stanlake, Marcus Stoinis, Andrew Tye, Adam Zampa.

Babar Azam fell one short of a maiden Test century after a farcical Azhar Ali run out as Pakistan put themselves well on course for victory over Australia in Abu Dhabi on day three. 

Fakhar Zaman and Sarfraz Ahmed came to Pakistan's rescue after a blistering spell of Nathan Lyon bowling had handed Australia early control of the second Test on day one in Abu Dhabi.

Usman Khawaja made a magnificent resilient hundred before Tim Paine and Nathan Lyon denied Pakistan as Australia produced a monumental rearguard action to draw the first Test in Dubai.

Pakistan needed seven

Aaron Finch will skipper Australia's Twenty20 team after being handed the captaincy ahead of the country's three-match series with Pakistan.

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