Chasing 328 to win, India were four for no loss in their second innings when rain forced an early stumps.
The duo put on 123 runs before Hazlewood picked up five cleaned India up.
Rain washes out final session as Rohit Sharma wicket gives hosts slight edge.
India are playing with their most inexperienced Test attack since 1933.
The duo battled through 40-plus overs and bat throughout the final session to deny Australia an inlet
India lost openers bid to chase 407 in the final session on Day 4 of the ongoing SCG Test on Sunday.