Left-arm spinner Matt Kuhnemann broke the 74-run opening stand when Rohit's backfoot punch went straight to Marnus Labuschagne at short extra cover.
Rohit, who made 35, left shaking his head after failing to convert the start into a big knock in perfect batting conditions.
Gill and Cheteshwar Pujara consolidated India's position even though runs were not easy to come by in the second session.
On a hot day, Australia captain Steve Smith used his quicks in short bursts and often tinkered with field setting to stem the flow of boundaries.
The run-rate plummeted and India endured a 16-over boundary drought which Gill eventually ended with back-to-back fours off Cameron Green.
The opener brought up his hundred with a four off Todd Murphy before bowing to the applauding crowd in celebration.
Murphy tasted success with the final delivery of that over when Pujara fell lbw for 42.
Gill started cramping up towards the end and was trapped lbw by Nathan Lyon after playing a tired-looking shot and missing the ball.
India need to win the match to seal their place in the final of the World Test Championship against Australia at The Oval in June.