An improved batting performance in the second innings by the host after conceding a 133-run first innings lead saw it set Andhra a target of 218 in 39 overs for an outright win.
Baba Aparajith made an unbeaten 108 while skipper Abhinav Mukund missed out on a ton, falling for 95 and Test opener Murali Vijay came back after retiring hurt yesterday after appearing to roll his ankle to score a sparkling half-century.
After a bright start, the visiting side faltered as Tamil Nadu bowlers exerted pressure in pursuit of victory.
K S Bharat led the way for Andhra with an enterprising knock of 64, which included five fours and two sixers while Ricky Bhui made 40.
However, after Bhui's exit with the score at 161, Test all-rounder R Ashwin and K Vignesh picked up quick wickets to put the brakes on the scoring.
The dismissal of Bhui and the first innings centurion B Sumanth by Vignesh and Ashwin Hebbar and B Ayyappa by Ashwin raised Tamil Nadu's hopes but time ran out for them.
The quick loss of wickets towards the end added to the excitement before Andhra finished at 198 for 7.
Earlier in the day, resuming at 112 for 2, captain Mukund and Aparajith scored briskly and took the score to 192 before the former fell to left-arm spinner Bhargav Bhatt.
Aparajith, who made a patient half-century in the first innings, played fluently and hit 10 fours in his knock.
Vijay, who has been out of the Indian side since the series against Australia owing to fitness-related issues, returned at the fall of the fifth wicket. He found his groove quickly and hit some superb shots, including one six.
The stylish right-hander fell to a catch by Ashwin Hebbar to occasional bowler DB Prashanth Kumar for 55.
Tamil Nadu declared after a flurry of boundaries by M S Washington Sundar and N Jagadeesan, leaving AP 218 to win.
Andhra got three points for gaining the first innings lead while the host had to settle for one point.
Tamil Nadu next plays Tripura here from October 14.
Brief scores (End of day 4): Group "C": Tamil Nadu 176 all out and 350 for 6 declared in 105 overs (Baba Aparajith 108 not out, Abhinav Mukund 95, M Vijay 55, Prithvi Raj Yarra 3 for 61)drew Andhra Pradesh 309 all out in 123.4 overs (B Sumanth 109, R Ashwin 4 for 71) and 198 for 7 in 41.4 overs (K S Bharat 64, Ricky Bhui 40, K Vignesh 3 for 34, R Ashwin 2 for 92) in Chennai. Points - Andhra: 3; TN: 1.
Madhya Pradesh 551 for 8 declared in 164 overs (Devendra Bundela 99, Shubam Sharma 196, Ankit Sharma 104) and 73 for 2 in 16 overs (Harpreet Singh Bhatia 44 not out) beat Baroda 302 all out in 79 overs (Yusuf Pathan 111, Irfan Pathan 80) and 318 all out in 76.1 overs (Yusuf Pathan 136 not out, A Sheth 109, Ishwar Pandey 5 for 40, Mihir Hirwani 3 for 77) by eight wickets at Indore. Points - MP: 6; Baroda: 0.
Tripura 194 for 8 declared in 68 overs (U U Bose 104, Dhiraj Singh 5 for 55) drew Odisha 18 for 1 in 5 overs at Bhubhaneshwar.
Points - Tripura: 1; Odisha: 1.
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