Starting the final day on 113 for 3 and chasing an improbable victory target of 788, Bengal were kept in the fight till the extended tea session by Tiwary (124), Shaw (118) and Ashok Dinda (52) before they folded up for 432.
Lanky pacer Ishwar Pandey once again led the bowling honours for MP with a haul of 4 for 93 to add to his first innings tally of 4 for 45, while debutant pacer Chandrakant Sakure finished with a match haul of six wickets that included his second innings 3 for 114.
When play started on the final day, the only point of interest was whether Bengal - similar to last year when they denied MP an outright win - could repeat the feat.
The loss of two wickets in successive overs pegged them back but Tiwary, who stroked his way to 14 fours and 3 sixes in 161 balls, and Shaw - who was the last batsman to be dismissed after facing 137 balls and striking 13 fours and four sixes - put on 108 for the sixth wicket to prolong the fight.
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After lunch, Shaw kept one end up, adding 58 runs with Pragyan Ojha (27) for the seventh wicket and 78 for the next wicket with Dinda, who used the long handle to smack ten fours in his 42-ball cameo.
The game ended when Pandey caught and bowled Shaw with the second new ball soon after dismissing Dinda while Sakure accounted for Veerpratap Singh.
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MP coach Harvinder Singh Sodhi exuded confidence for the tough semi-final clash against Mumbai following his side's crushing victory over Bengal
"You have to be very patient and you have to build partnerships. These are the two very important things in a five-day game. You have to follow all these things. This game has helped all our boys and prepared us well for the semi-final.
"It was also important because we were coming to play a five-day game after playing the one-day and T20 tournaments. So in the mental switch from that short format to the long format, I think we have done well in this game and that should also help us (against Mumbai)," he added.