Opener Gill, playing his second match of the series, featured in three 50-plus partnerships to help India, who lead the series 2-1, reach 289-3 at stumps.
Kohli was batting on 59, his first test half-century in 16 innings, with Ravindra Jadeja on 16 at the other end and India still 191 behind.
Hopefully we'll bat well tomorrow and get some big score for us, and then you know anything can happen on day five," Gill told the broadcasters.
"Hopefully, the wicket will help our bowlers and if it does, we'll be trying to win this match."
"The pitch was pretty good to bat on... It was important for us to bat big and keep picking the singles whenever possible."
Earlier, both the Indian openers signalled their attacking intent after they resumed on 36 for no loss at the Narendra Modi Stadium, which presented the best batting conditions in the series.
Gill stamped his class with an exquisite cover drive against Mitchell Starc, while Rohit Sharma disdainfully pulled the left-arm quick for a six as India reached the 50-mark in the 13th over.
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.
