Australia's first-time captain Steven Smith' century in the first innings helped his side beat India by four wickets in the second Test that ended in Brisbane on Saturday.

Smith lost the toss and his opposite number, MS Dhoni, chose to bat first on a pitch that assisted bowlers early on. India's batsmen, led by 144 from opener Murali Vijay, dominated much of the first day.

India's top and middle order got off to good starts, before they fell. Ajinkya Rahane's 81 helped the visitors post a sizeable 408 in the first innings.

Australia's debutant fast bowler, Josh Hazlewood, did the bulk of damage with the ball and claimed five wickets. Australia's top three provided their side a solid 121-run platform and put their side well on course to chasing India's total.

Following David Warner, Chris Rogers and Shane Watson's departure, captain Smith came to the fore. Smith's solid 133 was punctuated with 15 boundaries and it came from 191 balls. His innings was emblematic of his growth as both a batsman and leader.

Greg Chappell, in 1975, was the only other Australian batsman to score a century in his first innings as a first-time captain. This was Smith's sixth hundred in his 13 matches since August 2013, when Australia beat England at The Oval.

His heroics, and Mitchell Johnson's quickfire 88 from 93 balls, helped the hosts post 505 in their first innings, i.e 97 runs more than India.

Johnson, who went wicketless in the first innings, came back stronger in the second innings and wrecked India's strong middle order. He dismissed Virat Kohli, Ajinkya Rahane and Rohit Sharma in quick succession to leave India reeling at 86 for four, still 11 runs short of making Australia bat again.

India never recovered from the setback and crumpled to 224 in the second innings, leaving Australia just 128 runs to win the second Test.

Though Ishant Sharma and Umesh Yadav bowled impressively to dismiss six Australian batsmen in the second innings, the hosts claimed victory in just four days of Test cricket.

"The boys played some very good cricket the last four days and it's very satisfying to come out with a win. First day was very tough, the boys were dropping like flies. Credit to how they came out and bowled on the second morning," Smith said.

"First innings runs are crucial here and getting a lead of 90 was handy. Josh Hazlewood is an outstanding bowler and he's started extremely well for Australia. Mitchell Johnson, Mr. Reliable, as always. I don't think it was advisable [winding up Johnson], and that partnership really set the game up for us. It's always tough playing against India, they've played some extremely good cricket and we just won the key moments. It's been an amazing thrill over the last week to captain this side, the boys have been outstanding and backed me up nicely."