Resuming at the overnight score of 200 for four, Rahil Shah, who didn't bowl in the first innings, scalped four wickets for 38 runs, including that of V Cheluvaraj (88) to trigger Railways' collapse.
Railways lost their last six wickets for 40 runs inside 19 overs. The hosts lost their first wicket of the day in the fifth over when captain Mahesh Rawat (78) was trapped leg before by seamer J Kousik (2/45).
There was hardly any resistance from the other Railways batsmen, as Rahil cleaned up the tail with three more wickets to bundle out the hosts for 240 in 88.2 overs.
Set a paltry target of 77, Tamil Nadu lost a chance to secure seven points when captain Abhinav Mukund was bowled by Anureet Singh in the ninth over.
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But the visitors rode on Dinesh Karthik's 40-ball 43 to complete the chase in 23.2 overs.
Brief Scores:
Tamil Nadu: 328 & 77 for 2 in 23.2 overs (Dinesh Karthik 43; Anureet Singh 2/43) beat Railways 164 & 240 (V Cheluvaraj 88, Mahesh Rawat 78; Rahil Shah 4/38) by eight wickets.
Points: Tamil Nadu 6, Railways 0.