Powar, who scalped seven in the first innings, took three for 59 while medium pacer Ajit Agarkar dismissed four Bengal batsmen for 32 runs to ensure an outright victory and five points at the Jadavpur University campus ground, Salt Lake.
Resuming at the overnight score of 14 for no loss, Bengal were all out in the post tea session in 83.2 overs.
Skipper Rohan Gavaskar, who remained unbeaten at 70 (244 m, 164 b, 9x4), was the lone exception in an otherwise grossly indisciplined batting display.
Earlier, the hosts cheaply lost openers Arindam Das (11) and Nikhil Haldipur (21) with only 35 runs on the board.
Agarkar, who was not much successful in the previous innings, returned with a vengeance and broke the opening stand before picking up the wicket of Deep Dasgupta for nil.
It was then the turn of Powar to rip through the Bengal middle order. The off spinner used the bounce of the wicket to good effect to dismiss Sanjib Sanyal and Sourashis Lahiri, the principal scorers for Bengal in the first innings.
Mumbai, who had routed Andhra Pradesh by an innings in the last match, gained five points, including one bonus point for gaining innings victory to take their points tally to 12 from four ties. Bengal remained with 4 points from three matches.
Brief scores: Mumbai 552/7 decl.
Bengal 239 and 181 (R Gavaskar not out 70; A Agarkar 4/32, R Powar 3/59).