Shakib claimed 5-44 in the second innings to help bowl out Zimbabwe for 151, clinch the three-match series 2-0, and send Zimbabwe to the bottom of the test rankings.
He had figures of 5-59 in the first innings as Bangladesh took a 65-run lead, cutting down Zimbabwe for 368.
Shakib, who hit 137 in the first innings, joined England's Ian Botham and Pakistan's Imran Khan to take 10 wickets and score a century in a test. Botham and Imran both accomplished the feat in 1980 against India.
"It wasn't easy to score runs but difficult to get out, too, once you settled in. It was turning a lot on the last day. I put the ball in the right areas and it worked. It's a great feeling to lead a series 2-0 and hopefully we'll keep on doing this in the future series as well."
Shakib's rare achievement was complemented by fellow left-arm spinner Taijul Islam, 3-44, and legspinner Jubair Hossain, 2-42, as Zimbabwe was washed away by the spin-wave, losing its last five wickets for 14 runs.
Only No. 3 batsman Hamilton Masakadza stood tall, following his career-best 158 in the first innings with 61 in the second.
As long as he was at the crease on Friday, Zimbabwe had a glimmer of hope of drawing the match at least, after being set a target of 314.
But Shakib sparked Zimbabwe's collapse just after the tea break, dismissing Masakadza with one that got extra bounce and touched the shoulder of his bat to offer a simple catch at silly point.
Masakadza stuck five fours and a six in his 113-ball stay, falling at 137-6.
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