Karthik struck a defiant 217-ball 121 not out, his fifth first-class hundred and the season's first, while Subramaniam Badrinath (45 not out) also showed a lot of determination as both steered their side to a draw on the final day at the Feroze Shah Kotla Stadium.
Delhi have moved up to 11 points and third place on the table behind Odisha and Baroda, while Tamil Nadu are fourth on nine points.
Odisha's second successive victory after upsetting Karnataka by 65 runs at home and Baroda's thrilling one wicket win over Haryana in Lahli today have thrown open the group.
Meanwhile, having declared their first innings at 555 for four, the Delhi pacers led by Parvinder Awana (4/53), bundled out the visitors for a meagre 226 in their first essay last evening.
Resuming their second innings at an overnight score of two for no loss, Tamil Nadu, while following on with 327 runs adrift of Delhi's massive first-innings total, batted cautiously to deny the hosts a chance to secure an outright victory and grab a point from the drawn tie.
Karthik and Badrinath stitched an unconquered 103-run partnership for the third wicket after the visitors had lost opener Abhinav Mukund (38, 104 balls, 7x4) and Baba Aparajith (9).
With the possibility of a result looking unlikely, Delhi skipper Shikhar Dhawan and his counterpart, Lakshmipathy Balaji of Tamil Nadu, mutually decided to end the match nine overs after tea. More