Despite a valiant 78 by Raqibul Hasan, the Tigers innings folded on 254 in 44.2 overs in response to the home side´s huge 323-7, which is their highest total against the tourists. Their previous highest was 310-6 made in Dhaka in March 1999.
The result keeps the series alive as the Tigers now lead 2-1 after winning the first two games by eight wickets and 49 runs respectively.
Had Shakib Al Hasan´s men won it would have been their eighth in a row, one short of their record best in ODIs. Moreover, only their fourth overseas ODI series triumph.
Earlier, Bangladesh trounced Kenya 3-0 in 2006, outplayed Zimbabwe 3-1 in 2006-07 and last month inflicted a three-nil whitewash over West Indies.
Elton Chigumbura with his quickfire fifty was named man of the match.
The fourth match will be played at the same venue on Sunday.
Tawanda Mupawira set the tone with the dismissal of Tamim Iqbal first ball, and Bangladesh proceeded to stumble in the face of a stiff target.
The bowler also got the prized-wicket of Mohammad Ashraful in between Elton Chigumbura sent back promoted opener Naeem Islam for four.
Any thoughts of another amazing knock from Shakib Al Hasan faded after he fell 17 with the score on 39 in the eighth over.
Vice-captain Mushfiqur Rahim and Raqibul Hasan then staged a mini-fightback with 68 runs for the fifth wicket before Mushfiq was caught at long-on by Charles Coventry off Ray Price.
The left-arm spinner also claimed Mahmudullah Riyad (14) who was dismissed in similar fashion
Raqibul Hasan held the innings together before eventually bowled by Masakadza for 78 off 83 balls featuring four boundaries and two sixes.
Number nine batsman Mahbubul Alam helped himself to career-best 43-ball 57.
Ray Price finished with 3-34, Tawanda Mupariwa 3-32, Elton Chigumbura 2-46 and Masakadza 1-37.
Earlier, Hamilton Masakadza scored a maiden one-day hundred (102) to propel Zimbabwe to their record score. He also featured in a brilliant fourth-wicket stand of 142 with Brendan Taylor (94).
The stand was broken after the former was bowled by Syed Rasel.
Taylor, looking set to complete his first three-figure score in limited-overs cricket, before being run out by Shakib Al Hasan while trying attempting a second run.
Taylor took a backseat after Elton Chigumbura slammed 61 off 33 balls studded with five sixes and three fours. His fifty came off just 26 balls.
Stuart Matsikenyeri made a nine-ball 23 and Charles Coventry was run out for 22.
Shakib Al Hasan grabbed 2-65 while Mahbubul Alam was expensive with 2-84 from nine overs. Syed Rasel took 1-59
Zimbabwe, put into bat, lost both openers cheaply.
Mark Vermeulen was caught at midwicket by Mahmudullah Riyad for 10 off Mahbubul Alam in the fourth over.
The right-arm paceman also claimed Vusi Sibanda ( 0 ) after he was caught behind off the fourth ball of the second over.
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