Chasing a target of 170, Ibrahim Zadran led the way in early overs, unleashing an array of attractive strokes to get Afghanistan going.
After that, Rahmanullah Gurbaz backed his partner, opening his arms to power Afghanistan towards a win. The batter fell in the 10th over, with his team placed at 68.
Zimbabwe bowled with greater discipline from overs 11-20, picking up Sediqullah Atal (6) while 30 runs were added. But with an asking rate of close to two, Afghanistan batters could afford to play defensively and close in on the target.
Skipper Rahmat Shah partnered Zadran as Afghanistan inched closer to the target before the batters opened their arms in the 27th over, hitting two boundaries off Raza.
Wessly Madhevere eventually accounted for Rahmat (43) but Afghanistan managed to seal the chase in 35th over mark. Zadran remained unbeaten on 70.