Khawaja and Green forged a mammoth 208-run stand for the fifth wicket, the highest for either side in the bowler-dominated series, in perfect batting conditions especially in the wicketless morning session.
Ravichandran Ashwin claimed three wickets after lunch but Australia, who trail India 2-1 in the Border-Gavaskar series, would be pleased how they have fared after electing to bat.
Khawaja has faced 421 balls, most by an Australian batter in India, hitting 21 fours in his chanceless knock.
On a flat track where the ball did not really turn and reverse swing did not materialise, Khawaja and Green piled on the runs in the morning session.
Green illustrated his growing confidence hitting Umesh Yadav for three boundaries in an over and brought up his hundred with a four off Ravindra Jadeja.
The all-rounder took off his helmet and soaked in the applause sporting an ear-to-ear grin before Khawaja hugged him.
Ashwin (4-83) finally broke the stand when Green attempted a sweep shot and managed to glove the ball to wicketkeeper KS Bharat.
Four balls later, Carey played a slog sweep against the off-spinner and Axar Patel collected the top-edge at short third man.
Ashwin also removed Mitchell Starc but Khawaja remained on course for his maiden 200 in test cricket.
Australia players wore black armbands to honour skipper Pat Cummins' mother Maria who passed away overnight.
Steve Smith has been leading Australia in the absence of Cummins, who flew home to be with his mother after the second test in Delhi.
