Set 287 to win, India resumed at 115 for five on the final day and never threatened to pull off a miraculous victory, losing their last five wickets for just 21 runs.
They were dismissed for 140, with spinner Nathan Lyon claiming 3-39 to finish with eight wickets for the match and guide the home team to a drought-breaking success, their first in seven Tests spanning almost 10 months.
It was Australian captain Tim Paine’s first Test win in five matches since taking over from the suspended Steve Smith in South Africa, and also the first victory for new coach Justin Langer, coming in his hometown.
Australia’s previous Test win was against South Africa at St George’s Park in March.
It was during the following Test at Newlands that Cameron Bancroft was caught using sandpaper to alter the ball and Australian cricket was plunged into turmoil.
The scandal led to lengthy suspensions from Cricket Australia for Bancroft, Smith and opener David Warner and saw Paine appointed as skipper just months after being recalled to the side.
Australia’s best result in the four previous Tests since the scandal was narrowly hanging on for a draw against Pakistan in Dubai.
They had also won only six of 22 one-day internationals and Twenty20 matches since the scandal.
Having already lost star batsman, captain and first innings centurion Virat Kohli for 17 on the fourth day, during which he engaged in extended verbal jousting with Paine while the latter was batting, India’s hope rested on overnight batsmen Hanuma Vihari and Rishabh Pant.
- Tail folds -
However, Vihari added just four to his overnight score and fell to Mitchell Starc (3-46) for 28.
The right-hander tried to flick the ball through the leg side and only succeeded in ballooning a simple catch to Marcus Harris at midwicket.
Knowing he was running out of partners, Pant tried to force the issue but miscued a drive off Nathan Lyon low to midwicket, where Peter Handscomb dived to his left and took another excellent catch, having been the man that took the contentious catch in slips to remove Kohli in the Indian first innings.
His dismissal for 30 left only India’s notoriously fragile tail with exactly 150 needed and ended any hope of them pulling off an unlikely win on a lively pitch exhibiting spells of variable bounce.
Umesh Yadav lasted 23 balls until he tamely parried a return catch to Starc for two and India slid to 139 for eight.
Ishant Sharma was in no mood to hang around and backed right away, edging a Pat Cummins (2-25) delivery through to wicketkeeper Paine for a duck.
The last man to fall was Jaspit Bumrah, who went for a big shot and only succeeded in skying a chance back to bowler Pat Cummins.
The series now heads to Melbourne, with the famous Boxing Day Test starting on December 26 and India looking to regroup as they seek to win their first-ever Test series in Australia.
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