The hosts romped to their victory target of 115 in the second session
India spinner Ravindra Jadeja on Sunday returned career-best figures of 7-42 to help India take an unbeatable 2-0 Test series lead with a six-wicket thrashing of Australia inside three days of a dramatic match.
Jadeja, a left-arm orthodox bowler, teamed up with fellow spinner Ravichandran Ashwin to dismiss Australia for 113 in a morning session when the tourists' batting imploded, thanks to overusing the sweep shot on a tricky New Delhi pitch.
The hosts romped to their victory target of 115 in the second session, guaranteeing that they retain the Border-Gavaskar trophy in the four-match series.
They have won their previous three series against Australia and are now close to securing a spot in the World Test Championship final.
India lost skipper Rohit Sharma, run out after a fluent 31, and Virat Kohli, who surpassed 25,000 international runs during his innings, stumped on 20.
Nathan Lyon took two wickets to return a match haul of seven.
Cheteshwar Pujara stood firm with 31 in his landmark 100th Test to steer his team home with a winning four, as wicketkeeper-batsman Srikar Bharat, unbeaten on 23, looked on.
"We were prepared for them coming out and playing shots," Rohit said of his team's bowling plan.
"Our idea was to not panic and just hit the right areas, waiting for the mistake to happen, and that's exactly what happened."
He added: "So our focus was keeping it tight in the morning, and these guys (Jadeja and Ashwin) are the masters of bowling in these conditions."
Australia, who also lost the opening Test inside three days, crashed from their overnight 61-1 to be bowled out in 31.1 overs, after losing nine wickets for 52 runs in just over 90 minutes of mayhem.
Jadeja improved on his previous Test best of 7-48, adding to the three he took in the first innings. Ashwin grabbed the remaining three in the Australian second innings.
Off-spinner Ashwin struck in the first over of the day to get Travis Head caught behind for 43, three balls after the left-hander hit a boundary to add to his overnight score.
'This loss hurts'
Marnus Labuschagne attempted to take the attack to the opposition with the paddle shot and the reverse sweep, but was bowled by Jadeja for 35.
David Warner's concussion substitute Matt Renshaw looked clueless against spin in his eight balls at the crease, before he missed an attempted sweep, giving Ashwin another lbw.
Wickets fell like nine-pins and Lyon narrowly averted a Jadeja hat-trick. The bowler kept up the charge to wrap up the Australian innings, which started on a promising note near the end of day two.
"Everyone controls their own game, some balls just have your name," skipper Pat Cummins said on the overuse of the sweep. "But we need a review on the shot choice.
"Both games were disappointing, this one in particular," he added. "We were ahead in the game and that doesn't happen often in India. This loss hurts."
Man of the match Jadeja said the sweep shot was "not a good option" against him on this pitch, which saw low bounce.
Axar Patel set up victory with his counter-attacking 74 on Saturday, lifting India from a precarious 139-7 to just one short of Australia's first-innings total.
The left-hander put on a key 114-run eighth-wicket stand with Ashwin to turn the tables on Australia, who kept coming back with Lyon leading the bowling charge.
Lyon returned figures of 5-67 with his off-spin and was supported by fellow spinners Todd Murphy and debutant Matthew Kuhnemann -- both of whom took two each.
The third match will be played in Indore from March 1.