The pair – wearing black armbands following the death of skipper Pat Cummins’ mother – extended their unbeaten partnership to 177.
Both Green and left-handed Khawaja got the occasional boundary to take the total past 300 a low-scoring series which India lead 2-1.
Green, standing tall at 1.98m (6 feet and 6 inches), changed gears in the second half of the morning session as he smashed Umesh Yadav for three fours in one over to draw closer to his ton.
India’s pace bowlers, especially Yadav, looked listless with their line and length, while the usually wily spinners lacked bite.
Pace spearhead Mohammed Shami worked hard to add to his two wickets from day one but India remained wicketless in the first session.
Khawaja, who struck his first Indian Test ton on day one and 14th overall, has been key to Australia’s dominance after they elected to bat in the final match of the series.
The hosts need a win to clinch the four-match series and secure a berth in the World Test Championship final in June at The Oval.
Steve Smith is captaining Australia in Cummins’ absence.