A 190-run partnership between Karthik and Shankar laid the platform for a late assault, but TN remained circumspect.
Set a daunting target of 445 runs, Mumbai were 61 for no loss at stumps on day two of the semifinal.
Karthik made 113, while fifties from Shankar, Prasanna and Indrajith ensured that TN pile up 426/5.
Mumbai touched a new low as they were bundled out for 44, their second lowest innings total in the Ranji Trophy.
Vijay Shankar hit an unbeaten half-century on the opening day of the semifinal between TN and Maharashtra.
Collectively Maharashtra’s pacers have accounted for 114 opposition scalps this season. Tamil Nadu’s fast bowlers have only taken 38 between them.
Paceman Shardul Thakur will be Mumbai’s go-to man ahead of semifinal against Karnataka.
Thakur, Sandhu inspire 40-time champions to 204-run win over Delhi and a place in semis.
Vidarbha were left with a target of 411 runs and were staring at outright defeat when they lost four wickets.
Chasing 440 for a win, Delhi started on their overnight score of 110 for four but found little resistance.
Karnataka will take on Mumbai in the semifinal at its home ground in Bangalore.
Day marred by incident between players as Mumbai, Delhi go into final day of QF with game in the balance.
Karnataka virtually assured their place in the semis of the Ranji Trophy after setting formidable target of 683.
Herwadkar (161) survives two dropped catches, combines with Iyer to put team on firm footing on Day 3.
Tamil Nadu took an upper hand by reducing Vidarbha to 206 for six on the third day of their Ranji Trophy match.