Batting first, Gujarat scored a decent 248/8 with useful contributions from middle-order batsmen Chirag Gandhi (71) and Manprit Juneja (74). Tamil Nadu skipper Ravichandran Ashwin was the most successful bowler with 3/51 in 10 overs.
In reply, Tamil Nadu were all out for 217 in 47.3 overs as Axar's figures read 10-1-43-6.
India's limited overs specialist ran through the Tamil Nadu top-order despite India discard Abhinav Mukund carrying his bat through the innings with an unbeaten knock of 104.
From 84/0, Tamil Nadu slumped to 99/4 as the left-arm spinner struck four times in his first three overs.
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Karthik, along with Baba twins Aparajith (7) and Indrajith (1) were dismissed quickly. India's Test specialist Murali Vijay (0) also departed without opening his account.
Three of the four batsmen were stumped as they tried to play attacking strokes.
Tamil Nadu never recovered from the setback even though left-hander Mukund carried the fight till the end playing 142 balls and hitting six fours.
Mukund virtually had no support at the other end as Jasprit Bumrah finished the game with couple of fuller deliveries to polish off the tail.
Brief Scores: Gujarat 248/8 in 50 overs (Manprit Juneja 74, Chirag Gandhi 71, Ravi Ashwin 3/51)
Tamil Nadu 217 in 47.3 overs (A Mukund 104 no, Dinesh Karthik 41, Axar Patel 6/43). Gujarat won by 31 runs.