Chasing a target of 187, Zimbabwe were in trouble at 80-6 as Rishad (4-26) and fellow spinner Mahedi Hasan (3-24) doing most of the damage by striking at regular intervals.
The home side had a bit of a recovery with Ryan Burl hitting 29 while Sikandar Raza struck 28 and Brad Evans contributed 25 but Zimbabwe were eventually 152 all out.
Earlier, it was the visitors who posted a total of 186-5 in their 20 overs with both openers Saif Hassan and Tanzid Hasan both hitting half-centuries.
Hassan struck 55 while Tanzid scored 58 in an opening partnership of 120, but the late impetus into the innings was provided by Mohammad Saifuddin (31 off 10 balls) and Yasir Ali (22 from 12 balls).
The third and deciding game game with be played at the Queen's Sports Club in Bulawayo on Sunday.
Bangladesh head coach Phil Simmons admits his team "let ourselves down" after collapsing to 54 all out and a defeat in a three-day practice match ahead of the Test series against Australia.
The Proteas will travel to Namibia later this month for a T20I tri-series, that will also include Zimbabwe, which will then be followed by three ODI matches.
Australia top-order batter Marnus Labuschagne is well rested ahead of bumper 18 months of Test cricket.
Bangladesh received a welcome boost ahead of the Test series in Australia after Litton Das was declared fit and added to the squad for the two-match series.
