The win in Dhaka gave Bangladesh a clean sweep in the five-match ODI series against their fellow cricketing minnows.
The whitewash came after the hosts recorded a 3-0 win against the visitors in the preceding Test series.
Taijul bowled Tinashe Panyangara in the last ball of his sixth over and returned to trap John Nyumbu leg before and bowl Tendai Chatara in the first two balls of his next over to complete the hat-trick.
Shakib Al Hasan took the last wicket to return figures of 3-30 as Zimbabwe collapsed after a fine start. They lost their last nine wickets for 33 runs and were dismissed for 128 in 30 overs.
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Leg-spinner Jubair Hossain shared in the demolition, taking 2-41.
Hamilton Masakadza top-scored for Zimbabwe with 52 and shared a 79-run second-wicket stand with Vusimuzi Sibanda (37) -- the only high point in Zimbabwe's innings.
Panyangara and Chatara, who shared the five Bangladeshi wickets that fell, briefly raised the visitors' hopes.
The 28-year old middle-order batsman hit two fours off successive balls from seamer Solomon Mire to seal the rout and bring up his 11th fifty in the process.
Sabbir Rahman, 13 not out, supported Mahmudullah after Bangladesh lost their fifth wicket with the score on 93.
Chatara finished with 3-44 while Panyangara claimed 2-49.