Zadran accounted for Shimron Hetmyer , Rovman Powell and Carlos Brathwaite on successive deliveries of his fifth over as the Windies, chasing a revised target of 140 in 35 overs by the Duckworth-Lewis-Stern Method, slipped from 99 for five in the 20th over.
The team from a strife-torn nation then bowled the fancied opponents out for 110 in 26.4 overs for a morale-boosting win ahead of the main tournament.
Zadran, who had earlier accounted for Shai Hope, finished with outstanding figures of 7-1-26-4.
Left-arm spinner Sharafuddin Ashraf and wrist-spinner Rashid Khan picked up two wickets apiece, while Mohammad Nabi and Shahpoor Zadran bagged a wicket each.
For the Windies, Evin Lewis was the top scorer with 36, while Marlon Samuels scored 34. Chris Gayle (9), Shai Hope (1), Jason Mohammed (0), Hetmyer (1) and Powell (9) all missed out on useful batting practice on a good surface.
Earlier, a rain-break helped Afghanistan to recover from a precarious 82 for eight in 25.4 overs to a competitive 163 for nine in 35 overs. When play resumed, Gulbadin Naib and Samiullah Shenwari came out all guns blazing and added 81 runs in the remaining 9.2 overs to give their bowlers with something to bowl at.
Gulbadin Naib hit a 38-ball 48 with three fours and two sixes, while Samiullah Shenwari returned not out on 42 from 55 balls. For the Windies, fast bowlers Sheldon Cottrell, captain Jason Holder and Kesrick Williams bowled with a lot of aggression and fire to share seven wickets between them.
While Afghanistan and the Windies were able to hit the ground running, albeit in a reduced overs game, Ireland and Zimbabwe were not that lucky when their match at the Queens Sports Club was abandoned without a ball being bowled due to a wet outfield following morning rains.
Elsewhere, the Netherlands defeated Hong Kong by eight wickets, defending champions Scotland overpowered Papua New Guinea (PNG) by seven wickets and Nepal surprised the United Arab Emirates by five wickets.