Australia had begun the fourth day hoping to make a good fist of holding out for a draw but lost eight wickets for just 57 runs.
The tourists had begun the day on 74 for two, trailing by 192 runs, but they were bowled out for 131.
Australia had made 237 for nine declared in their first innings but when India replied with 503 they faced an uphill task.
Ravichandran Ashwin finished the second innings with five for 63 and Ravindra Jadeja three for 33 as India built on their eight-wicket win in Chennai to lead the series 2-0 with two Tests remaining.
Shane Watson (nine) was caught down the leg-side off the bowling of Ishant Sharma in the third over of the day and then skipper Michael Clarke (16) was bowled by left-arm spinner Jadeja.
Jadeja struck again in his next over when top scorer Ed Cowan was caught at slip for 44 after the ball rebounded off keeper MS Dhoni's pads. Then 111-5 became 111-6 as Moises Henriques was run out for a duck following a direct hit by Jadeja.
Debutant Glenn Maxwell (8) fell lbw to off-spinner Ashwin before Peter Siddle (4) and Matthew Wade (10) fell in consecutive deliveries to Jadeja and Ashwin completed the procession on the stroke of lunch by trapping James Pattinson lbw for one.
Clarke said he was more concerned with Australia's first-innings performances in both Tests and they must work hard.
"We won both tosses and the wicket has been at its best both times to bat and 237 is unacceptable. Our shot selection has been horrible," he said.
"I know you don't get better as a player by sitting on the couch and doing nothing.
"We're fortunate in regards to having eight or nine days before the third Test."