The hosts, who resumed at 260 for two, declared the innings in the final session of the day and in response to the huge 500-plus total, Karnataka were 26 for no loss as they safely negotiated the 10 overs.
Robin Uthappa (18) and KB Pawan (5) will resume the visitors' first innings tomorrow.
The 18-year-old Aparajith, the find of India's Under-19 World Cup triumph, resumed at his overnight score of 85 and went on to score 112 off 255 balls.
His overnight partner S Badrinath scored 72 before being caught by KB Pawan off Sunil Raju in the 13th over of the day.
Aparajith also departed soon as he was stumped off left-arm spinner K P Apanna.
Skipper Karthik and Ramaswamy Prasanna then continued the hosts' batting feast as the two rattled an unbeaten 200-run partnership for the fifth wicket.
Karthik's knock came off just 182 balls and had 18 boundaries, including four sixes.
Left-handed Prasanna supported his skipper well with his 72-run knock. He hit five boundaries including one shot over the fence in his long vigil at the crease.
Brief Scores:
Tamil Nadu 1st innings: 538 for four in 168 overs. (D Karthik 154 not out, B Aparajith 112; S Raju 2/148).
Karnataka 1st innings: 26 for no loss in 10 overs. (Robin Uthappa 18 batting).
