Pujara and Dhoni both fell trying to attack off-spinner Jeetan Patel, who finished with four for 100. Left-arm paceman Trent Boult chipped in with figures of 3-93.
Resuming on their overnight score of 307-5, Pujara and Dhoni enjoyed a trouble-free morning session, which was delayed for 25 minutes due to the threat of rain.
Batting at the number three spot vacated by the recently retired Rahul Dravid, the 24-year-old Pujara continued to display the cool temperament that took him to a maiden test century in his fourth appearance for India.
In Image: India's captain Mahendra Singh Dhoni, center, gestures as he stands next to Cheteshwar Pujara during the second day's play