
Nathan Lyon was the last man out at the Melbourne Cricket Ground, bowled by seamer Jasprit Bumrah for 41 off the 10th ball of the day.
It broke a dogged 10th-wicket partnership of 61 runs, with No 11 Scott Boland left not out on 15.
The pair added six more runs after the resumption, leaving India with a winning target higher than any team has successfully chased in the fourth innings of a Melbourne Test.
The record is held by England, who reached a winning score of 332-7 against Australia in 1928.
Marnus Labuschagne top-scored for the home side with 70, helping to revive an innings that was faltering at 91-6.
The exceptional Bumrah took 5-57 to give him nine wickets for the Test and 30 across the first four Tests of the series.
Fellow seamer Mohammed Siraj’s second innings figures were 3-70.
Overcast conditions are forecast for most of today but there is little chance of rain.
The five-match series is locked at 1-1, with the final match to be played in Sydney from Jan 3.