Having struck his sixth ODI century to help the hosts to 281-7 in Chittagong, Shakib returned 4-41 to help dismiss Zimbabwe for 194 in the opening contest of their five-match series.
Bangladesh were therefore able to follow up their three recent Test victories over Bangladesh with a first ODI triumph in 383 days.
Shakib struck 101 from 99 balls and received able support from captain Mushfiqur Rahim (65) and Sabbir Rahman (44 not out from 25 deliveries) as Bangladesh posted an imposing total having been inserted.
In reply, Brendan Taylor (54) and Hamilton Masakadza (42) were the only batsmen to offer any resistance as Zimbabwe collapsed from a promising position, losing their final six wickets for 48 runs.
The tourists enjoyed initial success with the ball when reducing Zimbabwe to 31-3 with the aid of two wickets from Tendai Chatara (2-48).
However, Shakib steadied the ship alongside Mominul Haque (31) and then went on to add 148 for the fifth wicket with Mushfiqur.
Shakib, particularly strong square of the wicket on the off side, gradually accelerated as his innings progressed, reaching 50 from 57 deliveries and then pressing on to three figures from a further 38 balls.
He was eventually held at long-on off Tafadzwa Kamungozi (1-40), and Mushfiqur departed in the 48th over, but Sabbir provided further late impetus with three fours and three sixes.
Shakib then set about undermining Zimbabwe's reply, striking twice in his second over to remove Sikandar Raza (15) and Vusi Sibanda (nought).
Masakadza and Taylor helped their side recover, but the loss of the latter in the 30th over triggered an all too familiar collapse.
Mashrafe Mortaza (2-33), Arafat Sunny (2-22) and Mahmudullah (2-40) all chipped in to support Shakib as wickets fell at regular intervals.
The two teams will meet again in Chittagong on Sunday for the second game of the series.