Led by opener Gugale's 56 not out from 100 balls (11x4) in an unbroken 90-run stand with Chirag Khurana (36 batting from 77; 7x4), Maharashtra closed the day on a positive note.
The last season's runners-up still have an improbable task in hand, needing 440 runs to secure a first innings lead and ensure a final berth in the match heading towards a draw.
Rangarajan was left stranded at the other end with 67 not out (147 balls) as Tamil Nadu batted 226.4 overs spanning 16 hours and 40 minutes at a run-rate of 2.42.
Earlier Sanklecha (3/115) dismissed the two overnight batsmen Baba Indrajith (69) and Ramaswamy Prasanna (72), both caught at the slip cordon by Harshad Khadiwale, with addition of 20 runs in the day.
Maharashtra started scoring freely from ball number one with Gugale slicing Parameswaran through third man boundary.
Gugale lost his senior opening partner Khadiwale (14) early when the latter's defence was breached by Laxmipathy Balaji's incoming delivery. But Khurana gave Maharashtra some ray of hope.