Tamil Nadu was 112 for 2 in the second innings with Mukund batting on 52 in respone to Andhra's first innings total of 309.
They had an injury scare when Test opener Murali Vijay retired hurt when on 13 after appearing to have rolled his ankle.
Resuming at 231 for 7, Andhra extended their lead as Sumanth in the company of Shoaib Mohammed Khan added a further 52 runs as the host's misery continued.
Khan fell for 43, a crucial knock as it helped his team build an important lead, when he was leg-before wicket to Ravichandran Ashwin.
Sumanth continued to defy the TN bowlers and reached a well-deserved century of 254 balls.
He was the last man to be dismissed as Ashwin when M S Washington Sundar held on to a catch.
His 280-ball knock contained five fours and one six and went a long way in making sure of first innings points for his team as the match appears headed for a draw.
Ashwin finished with 4 for 71 for his efforts while K Vignesh scalped three wickets.
The home side began their second innings cautiously and Vijay seemed in good touch, before retiring hurt.
The left-handed Mukund looked solid and hit four boundaries in his half-century.
Andhra enjoyed success when one-drop batsman M Kaushik Gandhi was caught by K S Bharat of the young left-arm paceman Prithvi Raj Yarra for 7.
Baba Indrajith, who came in at No. 4 put on 40 runs with the skipper, before perishing off the bowling of Bhargav Bhatt for 16.
Baba Aparajith replaced his twin and ensured that the team ended the day without any further loss of wickets but trailing by 21 runs.
Brief scores (End of day 3): Group "C" Tamil Nadu 176 all out and 112 for 2 in 54 overs (Abhinav Mukund 54 batting) vs Andhra Pradesh 309 all out in 123.4 overs (B Sumanth 109, Ashwin Hebbar 64, Shoaib Mohammed Khan 43, K S Bharat 32, R Ashwin 4 for 71, K Vignesh 3 for 73, L Vignesh 2 for 42) in Chennai.
Madhya Pradesh 551 for 8 declared in 164 overs (Devendra Bundela 99, Shubam Sharma 196, Ankit Sharma 104, Harpreet Singh Bhatia 32, A Sheth 2 for 90, Swapnil K Singh 3 for 136) vs Baroda 302 all out in 79 overs (Yusuf Pathan 111, Irfan Pathan 80, Ishwar Pandey 2 for 44, Avesh Khan 2 for 75, Ankit Sharma 2 for 75) and 41 for 1 in 17 overs (Aditya Waghmode 31) at Indore.
Tripura 6 for no loss in 2 overs vs Odisha at Bhubhaneshwar.
First Published: October 8, 2017, 7:18 PM IST