Priyank Panchal, the highest run-scorer in the Ranji Trophy, and Dhruv Raval (39) restored calm with some positive strokes during the course of their 55-run partnership.
It took a fine delivery from Pankaj to dislodge Panchal - the ball pitched on middle and off and seamed away and the outside edge was caught by Karun Nair at first slip.
In the penultimate over before lunch, Parthiv attempted to punch Kaul off the back foot, but the ball was closer to his body than he anticipated and the resultant inside-edge found the stumps.
But Gujarat lost momentum once again, as Pujara introduced part-time offspinner Akhil Herwadkar to bowl the last over before tea, and he struck with his second delivery.
Rest of India made a few fielding lapses in the final session, as Kaul and Karun dropped straightforward chances offered by Karan Patel and Mohit Thadani respectively.
Kaul, who hurt his ring finger on his right hand while attempting the catch and went off the field, returned to make amends by dismissing Thadani.
An over earlier, though, Chintan Gaja was caught off a deflection off the keeper's pads and held by Manoj Tiwary at first slip, but umpire Virender Sharma turned it down.
Chaudhary swung his bat around for a few raspy hits before a Rest of India fielder - Manoj Tiwary - finally held on to a catch.
For most of the second session, seamers Chintan Gaja, Ishwar Chaudhary and debutant Mohit Thadani bowled with two point fielders to Pujara, and tried to provoke him into playing a loose stroke outside off.
Karun's first few runs came off inside-edges to the leg side; he briefly looked comfortable when he struck two cover drives for fours off successive deliveries from Hardik.
Soon, Hardik trapped Kuldeep Yadav lbw after the batsman, initially shaping for the sweep before changing his mind, failed to get his bat down in time.
Except for a typically sturdy 86 from captain Cheteshwar Pujara, there were few contributions of substance from a powerful batting line-up, as Rest of India fell from 136 for 2 to 192 for 9.
This time Manoj Tiwary, Rest of India's best slip fielder in this game, moved to his right to pocket his 100th catch in first-class cricket.
Nadeem's first wicket came under controversial circumstances when Gujarat captain Parthiv Patel (32) was adjudged caught at short leg by umpire Virender Sharma despite the ball being nowhere close to either his bat or glove.
Gujarat's momentum wasn't altogether lost was due to Gandhi, who batted with three stitches on his hand after sustaining an injury during catching practice before start of play.
Mohammed Siraj, the Hyderabad seamer, who was impressive all day, had Juneja hanging his bat at one outside off stump and Saha completed a simple catch.
Gujarat slumped from 126 for 2 to 184 for 6 as Nadeem worked around Gandhi by first bowling Karan and then removing Thadani and Chintan Gaja in the space of four overs.