Paceman Safyaan Sharif defended 14 runs in the game's final over by bowling Wellington Masakadza and running out Tendai Chatara as the visitors finished on 134 for nine.
Brendan Taylor will play his last match on Monday, September 13, 2021, against Ireland.
Brendan Taylor, Craig Ervine, Sean Williams return as Zimbabwe name squad for Ireland, Scotland tours
Taylor was rested for T20Is against Bangladesh while Williams and Ervine missed out on the series following their contact with people who tested positive for coronavirus.
Zimbabwe men's cricket team's tour to Ireland to include three ODIs matches and five T20Is while women's team plays Thailand at home.
Naim struck an unbeaten 63 from just 51 balls, with six fours, while Sarkar hit two sixes and four fours in his 45-ball 50 which was ended by a fine piece of work by wicketkeeper Regis Chakabva.
The Bangladesh tour will commence with a one-off Test followed by three ODIs, which are part of the World Cup Super League.
27-year-old Ryan Burl, a left-handed middle-order batsman, who has played three Tests, 18 ODIs and 25 T20Is, tweeted a picture of his shoe, a glue stick and some tools to fix it.
Zimbabwe only got 138-7 in reply after Usman Qadir's 3-29 thwarted the home team at Harare Sports Club and gave Pakistan an 11-run victory.
Heath Streak was banned from all cricket for eight years after he accepted five charges of breaching the ICC Anti-Corruption Code.
Ntini, 40, who played 101 Tests for the Proteas, has held the responsibility of bowling coach since January 2016 for a term of two years.