Mukund made 122 off 186 balls with the help of 11 boundaries, while Indrajith scored 138 off 169 deliveries with 13 fours and one six to set the platform for Tamil Nadu's total in the second innings.
Mumbai's first-innings total was revised to 411 when they were awarded five penalty runs due to Tamil Nadu's batsmen running on the pitch in the 74th over. That meant their target became 251 from the 256 Tamil Nadu had set.
The match is interestingly poised as Mumbai still need 246 runs to win with a full day's play remaining for Tamil Nadu bowlers to bundle out their opponents and enter the final of the Ranji Trophy for the ninth time in the history of the tournament.
Having conceded the first innings lead on the third day yesterday, Tamil Nadu had no option but to push for an outright victory.
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Tamil Nadu was also helped by some patchy fielding from Mumbai players who faltered when put under pressure.
Mukund and V Ganga Sridhar Raju (28) shared 64 runs for the opening stand before Balwinder Sandhu got the first breakthrough in the form of Raju.
But then Indrajith joined hands with Mukund and the duo played aggressively and piled up 185 runs for the second wicket to push Tamil Nadu forward.
For Mumbai, Sandhu (2/67) and Vijay Gohil (2/110) picked up four wickets between them.
Brief Scores:
Brief Scores:
Tamil Nadu: 305 & 356 for six in 78 overs (Baba Indrajith 138, Abhinav Mukund 122; Balwinder Sandhu 2/67).
Mumbai: 411 & 5 for no loss in 5 overs.