Taskin followed his 3-14 in the opener with 2-18 as Zimbabwe were restricted to 138-7 after Bangladesh captain Najmul Hossain Shanto won the toss and chose to field.Â
Bangladesh reached 142-4 in 18.3 overs in reply with Towhid Hridoy hitting a 25-ball 37 not out.
Mahmudullah, who confirmed the victory with an elegant cover-drive for a boundary, was unbeaten on 26 off 16.
Shanto said: "Bowlers did very well once again but it wasn't easy for the batters. There are a lot of areas we can improve."
Bangladesh beat Zimbabwe in the first game by eight wickets and made no changes for the second T20.
When openers Litton Das and Tanzid Hasan put on 41 runs, it appeared that Bangladesh's chase would be an easy one but Luke Jongwe (2-35) put up a fight. Pacer Ainsley Ndlovu, one of three changes for Zimbabwe, broke through with the wicket of Tanzid, who played a match-winning 67 not out in the first game.
Tanzid was dismissed on 18 after failing to execute his slog-sweep shot properly.
Jongwe removed Shanto (16) and Das (23) in four balls and, when pacer Richard Ngarava got the better of Jaker Ali (13), Bangladesh was 93-4 in the 14th over. Hridoy and Mahmudullah then added 49 runs for the victory.
Earlier, Johnathan Campbell, the son of Zimbabwe's former captain Alistair Campbell, hit a debut 24-ball 45. Brian Bennett was not out on 44.
Mahedi Hasan (1-18) and Rishad Hossain (2-33) ripped through the middle order as Zimbabwe lost three wickets including captain Sikandar Raza (3) for six runs to go from 30-1 to 36-4, and then 42-5, before Campbell and Bennett offered resistance.
Raza said: "It is still the same story as we keep on shooting ourselves in the foot. One can only hope we can learn eventually. The brand of cricket has been really poor especially in the first 10 overs of the innings and that hurts me a lot."
The third match is on Tuesday.
