India wicket-keeper KS Bharat endured a torrid opening hour behind the stumps and floored a waist-high sitter after Head, then on seven, had edged Umesh Yadav.
Head kept playing his shots but did not get his timing right against Ravichandran Ashwin and was caught at mid-on by Ravindra Jadeja.
India tasted further success largely because of Marnus Labuschagne's penchant to occasionally get stuck in the crease.
The right-hander, currently the top-ranked test batsman, pushed at a Mohammed Shami delivery only to drag it on to his stumps.
Khawaja, who brought up his 50 with a four off Shami, and Smith looked largely untroubled against the Indian attack.
The morning session crowd included Indian Prime Minister Narendra Modi, after whom the stadium is named, and his Australian counterpart, Anthony Albanese.
India, who lead the series 2-1, need to win the match to join Australia in the final of the World Test Championship at The Oval in June.