India scored 84/0 at tea on day 2 taking the lead to 130.
Jaiswal and Rahul remained unbeaten at 42 and 34 runs respectively.
Earlier, Jasprit Bumrah's fifer powered India to bowl out Australia for 104.
Bumrah picked five wickets for 30 runs. He was aptly supported by Harshit Rana and Mohammed Siraj who picked three and two wickets respectively.
India were bowled out for just 150 on day one.