The 22-year-old left-armer bowled Tinashe Panyangara off the last ball of the 27th over and then trapped John Nyumbu leg-before and bowled Tendai Chatara off successive deliveries at the start of his next over to take a split hat-trick.
Islam finished with four for 11 in seven overs as Zimbabwe, trailing 4-0 in the series, were shot out for 128 after choosing to bat in the fifth and final game at the Sher-e-Bangla stadium.
Islam is the fourth Bangladeshi and the 45th bowler to claim a hat-trick in one-day internationals, but the first to do it on debut.
He took 25 wickets in five Tests before being given a chance in the one-day format. – AFP