Fickle weather on day 4 prevented India from closing in on a big win in the 4th Test but they were well on course for their maiden series victory in Australia.
Australia were placed at 6-0 in 4 overs after Kuldeep Yadav's five-wicket haul in his maiden Test Down Under helped India bowl the home team out for 300 in the first innings.
Marcus Harris (2) and Usman Khawaja (4) were the unbeaten batsmen with Australia still trailing by 316 runs.
Hazlewood and Mitchell Starc (29 not out) then added 42 runs for the 10th wicket as Australia reached 300 despite another pitiful batting display.
India have an unassailable 2-1 series' lead after winning the first Test in Adelaide by 31 runs and the third Test in Melbourne by 137 runs.