Resuming at 256 for three, Baroda's last seven batsmen could add just 106 runs to their overnight score.
Last night centurion Kedar Devdhar failed to add to his overnight score of 104 as he became a run out victim.
On the other hand, Aditya Waghmode, resuming at 87, (113) completed his century before becoming Fallah's victim.
While Mundhe returned with figures of four for 72, Fallah picked up his three wickets giving away 86 runs.
In reply, opener Harshad Khadiwale remained unbeaten on 69 to guide Maharashtra to 131 for three at stumps.
Ankit Bawne was the other not out batsman on 26.
Mutuza Vahora and Gagandeep Singh picked up a wicket each for Baroda.
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Maharashtra still trail Baroda by 231 runs with seven wickets at hand.
Brief Scores:
Baroda: 362 all out in 130.4 overs (Aditya Waghmode 113, Kedar Devdhar 104; Shrikant Mundhe 4/72).
Maharashtra: 131 for three in 45 overs (Harshad Khadiwale 69 not out, Ankit Bawne 29 not out; Mutuza Vahora 1/6).