Opting to bat, the visitors were off to a disastrous start as opener K.L. Rahul's (2) thick edge was superbly taken by Aaron Finch at third slip off a Josh Hazlewood delivery with just three runs on board.
Soon, Murali Vijay (11) also followed his partner after falling in the seventh over, leaving India at 15/2.
With the addition of just four runs in the visitor's scorecard, Kohli followed for three to deepen India's troubles.
Pujara and Rahane (13) then tried to put things back in control, adding 22 runs for the fourth wicket, however, Hazlewood struck again in the the 21st over to dismiss the latter.
Rohit and Pujara then saw out the rest of the session as India crept past the 50-run mark and finished the session at 56/4.
The duo looked solid after the break as well as Pujara looked to dig in and the Mumbaikar taking on the opposition as he reached 37 off 60 balls, hitting three sixes and two fours before attempting a silly shot and falling to Nathan Lyon to further deepen India's woes.
He tried to hit one out of the park and all he could do was hold out to Marcus Harris at deep square leg as India were reduced to 86/5.