Chasing 226 for victory, Mumbai inched to the target but were precariously placed at 155 for seven at stumps in their second innings, still 71 runs short.
Ramesh Powar remained unbeaten on two, while Nilesh Kulkarni was yet to open his account.
Off spinner Jadhav claimed the crucial wickets of Vinit Indulkar and Amol Mazumdar, while leg-spinner Bahutule sent back the formidable Nishit Shetty and Abhishek Nair as Maharashtra made a remarkable comeback for the second time in the match.
After being bowled out for a paltry 187 in their second innings 19 minutes before lunch, Maharashtra fought their way back as Mumbai lost wickets at regular intervals.
Only a 60-run partnership for the fourth wicket between Indulkar and Muzumdar and a 57-run fifth wicket partnership between Muzumdar and Shetty brought hope of victory to the hosts at one stage, after they were 35 for three.