It was a matter of survival for Bengal as they finished the final day's play at 198 for seven with Saha remaining not out on 38 off 152 balls hitting five fours in the process.
Saha was let off on 7 by Kshemal Waingankar off medium pacer Nayar, who was on the rampage with the ball as he finished with incredible figures of six for 13.
Mumbai now have 10 points from four games and are third in the group behind Punjab and Madhya Pradesh while Bengal with seven points languish at the sixth place in the nine-team table.
Chasing a target of 391 was out of question as Bengal batsmen defended doggedly throughout the day scoring only 151 runs in 90 overs.
Nayar was in the middle of a deadly spell of 12-6-12-4 when the other frontline bowlers failed to make an effect on the rival batsmen when Saha was given a 'life'. Nayar again raised the home team's hopes of an outright victory when he struck twice in 4 balls with the new ball.
But Saha, who faced 126 balls after his escape and was reprieved for the second time by Avishkar Salvi on 21, ensured a draw for his team in the company of tail-ender Veerpratap Singh (0 not out in 19 balls and 35 minutes).
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Bengal had commenced very well this morning from 47 without loss with half centuries from openers Arindam Das (54) and Rohan Banerjee (59) to be 116 for no loss just before lunch before Nayar effected the breakthrough to dismiss Banerjee and trigger a post-lunch collapse.
Nayar, who hit half centuries in both the innings, finished with third five-wicket haul but did not get adequate support from the other bowlers.
Brief scores: Mumbai 297 and 294/5 decl; Bengal 201 and 198/7 (Arindam Das 54, Rohan Banerjee 59, Wriddhiman Saha 38 not out, Abhishek Nayar 6/13). Match Drawn. Mumbai 3; Bengal 1.