Half-centuries by Baba Aparajith (59 batting, 139 balls) and Baba Indrajith 58 (120 balls, five fours, one six) helped steady the ship for Tamil Nadu after it had slipped to 74 for 3.
Skipper Abhinav Mukund, from whom a lot was expected, failed in the crunch game,falling to Dhruv Patel for just six.
The other opener N Jagadeesan had been dismissed earlier, caught by Deepak Hooda off Lukman Meriwala's bowling for 7.
Aparajith and Indrajith came together to put on 73 runs as the visitors attempted to rebuild after the top-order failed to get going.
Indrajith, who has been in good form this season, struck five boundaries and hoisted one over the ropes before Kakade dismissed him for 58.
Aparajith, who too has been among the runs for TN, lost the talented, young M S Washington Sundar (12), who edged Kakade to the wicket-keeper M G Patel.
Tamil Nadu is still 83 runs behind in this must-win game.
Earlier, resuming at the overnight 254 for 8, the home side added a further 55 runs to the total. Swapnil needed eight balls to move from 94 to a well-deserved century.
He guided the No.10 and No.11 batsman to take the score past 300 and used the long handle to good effect. He hit five more sixes to take his tally to eight and also slammed 13 fours before being the last man out for 144 (226 balls).
At Indore: Odisha 147 all out in 52.2 overs (Shantanu Mishra 60, Chandrakant Sakure 4 for 42) 18 for no loss in 10 overs vs Madhya Pradesh 388 all out in 115 overs (Rajit Patidar 123, Devendra Bundela 62, Puneet Datey 56, Govinda Poddar 7 for 102).
At Mumbai: Tripura 195 all out in 60.4 overs (M B Mura Singh 43, Akash Parkar 5 for 32) vs Mumbai 421 for 8 in 111 overs (Jay Bista 123, Siddhesh Lad 123, Aditya Tare 67, Dhawal Kulkarni 50 batting, Mura Singh 5 for 71).
Disclaimer: No Business Standard Journalist was involved in creation of this content
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