The tourists, trailing by 400 runs after the first innings, were bowled out for just 181 in their second knock, 35 minutes after tea on the fourth day. Javagal Srinath, the seamer whose two-wicket burst in the first over of the match on Wednesday rocked Australia's start, finished with three victims in each innings.
Australia's hero in defeat was their pugnacious vice-captain, Steve Waugh, who defied a painful groin injury for three hours to make 33.
India's 18th win in their last 27 home Tests ended Australia's run of nine successive series wins under Mark Taylor since 1994. Despite that impressive record, which earned them the tag of unofficial world champions, the Australians remain vulnerable in the Indian sub- continent. The last time they lost a Test series was in Pakistan in 1994. Taylor's men also suffered a seven-wicket defeat by India in a one-off Test in New Delhi in 1996.
The Aussies, who lost the first Test in Madras by 179 runs, once again paid the price for woeful batting. They were skittled out for 233 and 181 on a good wicket whereas India amassed their highest score against Australia of 633 for 5 declared.
The Australians were reduced to 91 for 5 in their second innings before Waugh and Ian Healy fought back with a 42-run stand for the sixth wicket. The pair batted for most of the afternoon before Healy was unlucky to be adjudged leg before to Srinath after making 38. Krish Parthasarthy, the Indian umpire standing in his first Test, took no time in raising his finger even though television replays suggested the ball may have missed leg stump.
The Australians, who lost just one wicket in the post-lunch session, slumped in the first over after tea when Kumble grabbed the wickets of Shane Warne, who scored nine, and Gavin Robertson for a duck. Kumble then trapped Waugh leg before to end Australia's resistance.
Taylor and Greg Blewett had earlier advanced the overnight score of 38 for 1 to 55 before two wickets in as many overs left the tourists on the back foot. And when the opener Taylor was run out for 45, the top score of the innings, there was no way back.
Australia, meanwhile, have recalled Michael Bevan to join their injury- hit tour party as Waugh struggles for fitness ahead of the third and final Test, which starts in Bangalore on Wednesday. Bevan was in the unusual role of television commentator at a triathlon event in Queensland when he received the selectors' call.Reuse content