Spinner Steve O'Keefe finished with 12 wickets as Australia ended India's 19-Test unbeaten streak with a crushing 333-run triumph within three days in Pune.
O'Keefe followed up his first-innings six for 35 with identical figures in the second as the hosts were skittled for 107. Fellow spinner Nathan Lyon snared the other four wickets.
Australia captain Steve Smith had earlier posted his 18th Test hundred - his first in India - to help his team pull away to 285, setting the home team a daunting victory target of 441.
The result, in the first Test of a four-match series, was Australia's first win on Indian soil since 2004.
