Captain Virat Kohli said India were the better team and deserved to win after the tourists a dramatic finish to defeat a gallant Australia in the first Test in Adelaide.

India withstood a nervy finale at Adelaide Oval, where Kohli's men prevailed by just 31 runs as the visitors won the opening Test of a campaign on Australia soil for the first time on Monday.

Australia needed a record fourth-innings run chase to claim victory and despite falling to 156-6 and 235-9 in pursuit of 323, the home side came within a whisker of achieving the improbable before Josh Hazlewood was dismissed with the final ball before tea.

Tension was building prior to Ravichandran Ashwin's match-clinching breakthrough – Kohli visibly agitated as India's search for an historic win was thwarted by an inspiring rearguard display from Australia.

Kohli, however, insisted India were the superior outfit as the series heads to Perth for the second Test, starting Friday.

"It's important to stay calm. The odds were stacked up against them as soon as we got Pat Cummins out," Kohli said during the post-match presentation.

"I wouldn't say I was cool as ice but you try not to show it. It was just a matter of one mistake or one good ball. Super proud to have four bowlers and take 20 wickets to win this Test match. It's up to our batsmen to step up in this series. Pujara and Rahane stood up in this match.

"I thought we were the better team and deserved to win. I think when they bat together like that they are our most solid pair. I think it took a lot of grit and determination to put us past Australia.

"I think our middle order and lower order could've done better. These things are things to keep in mind for Perth. But if you had given me 1-0 up after the first game I would've taken that."

Cheteshwar Pujara was named man of the match after his 123-run display in the first innings, which he followed up with 71 in the second.

"I think playing here before has helped me a lot," Pujara added. "I think what has helped me is the preparation. Ultimately winning the Test match credit to all the bowlers.

"The first innings lead of 15 gave us the belief batting in the second innings. I always back my ability and I've got enough experience."

Head coach Ravi Shastri was pleased with "cool, disciplined, patient" India as they built a 166-run lead over Australia after three days of the first Test.

The tourists took an advantage into the second innings in Adelaide after bowling out Australia for 235 and then set about stretching their lead, first-innings centurion Cheteshwar Pujara again starring with an unbeaten 40.

Pujara partnered captain Virat Kohli (34) in a third-wicket stand of 71, while opener KL Rahul also contributed 44 runs, and Shastri was very happy with India's attitude throughout Saturday's play as they reached stumps with seven wickets still in hand.

"We'll take that," Shastri told FOX. "It was a good hard day's Test cricket. I thought we did well to wrap up the [Australia] innings quickly. We kept our cool, we were disciplined, we were patient.

"Then the same applied when we went out to bat. When we lost a couple of wickets, I think that partnership between Virat and Pujara was crucial. They added about 60 runs [actually 71].

"I would still say there's work to be done. But if you asked me at the start of the day, 'Would you take this?' I will take it."

Australia were similarly optimistic at the close of play, even with India well placed on 151-3.

Paceman Mitchell Starc said: "Apart from KL, who took us on a bit and got away with a few, I think we've been very good with the ball. It makes for an interesting last two days."

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 took it upon himself to step up after his India team-mates crumbled in the first Test against Australia on Thursday.

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

Teenager Prithvi Shaw scored a record-breaking century on his Test debut in Rajkot as India dominated West Indies on the opening day of the two-match series.

India batting coach Sanjay Bangar hailed a composed display from Cheteshwar Pujara as his first Test century in England helped the tourists claim a narrow lead. 

Cheteshwar Pujara tormented England with an unbeaten 132 to give India a narrow but potentially priceless advantage in the fourth Test at the Rose Bowl. 

Jonny Bairstow remains hopeful he will be able to bat again for England in the third Test against India despite suffering a fractured finger on day three at Trent Bridge.

Becoming just the fourth India team to win a Test series in England would be special for all the players, Cheteshwar Pujara has said.

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