The pair participated in a 102-run opening wicket partnership to put Bangladesh on their way to a comfortable victory as they chased a 153 goal for victory with seven balls to spare.
Naim finished with 63 not out, while Sarkar reached 50 before running out.
Zimbabwe, which won the draw, got off to a good start with Regis Chakabva transferring his ODI form to the T20 format and scoring 43 to guide Zimbabwe to 91-3 after 10 overs.
But they added just 61 more runs as the wickets fell in the next nine overs and they were thrown with one to spare. Mustafizur rahman took 3-31.
The teams meet again in the three-game series on Friday and Sunday. Bangladesh beat Zimbabwe in their only test this month and clinched a 3-0 victory in this week’s one-day international series.