Zimbabwe, victors in the first two encounters of the four-match series, looked to have set the tourists an imposing total in Bulawayo on Tuesday, as Hamilton Masakadza (84), Brendan Taylor (53) and Sean Williams (49) helped the hosts reach 261-8 from their 50 overs.
But strong performances from several of Afghanistan's batting line-up assured that they posted 264 with two balls to spare.
Javed Ahmadi's 56, Mohammad Nabi's quickfire 42 off 40 balls and Dawlat Zadran's 24 from just seven deliveries all proved pivotal in swinging the game in Afghanistan's favour.
After Sikandar Raza had been removed by Zadran (2-49) for just 11, Masakadza and Zimbabwe captain Taylor steadied the ship with a fine partnership of 109.
That stand guided Zimbabwe to a seemingly commanding position of 145-1, but, despite the best efforts of Taylor and Williams, meaningful partnerships down the order proved more difficult to come by as Afghanistan fought back with the ball.
Zadran, who also ran out Taylor, was the star of Afghanistan's performance in the field and was just as effective with the bat in guiding the visitors to victory.
Following the superb efforts of Ahmadi and Mohammad Nabi, Zadran came to the crease with Afghanistan seemingly teetering on 229-7 when the latter was run out by Malcolm Waller.
However, Zadran showed no signs of nerves, smashing four sixes, the final one coming with two balls to spare to seal only the second win against a Test-playing nation for Afghanistan.
The tourists will attempt to level the series in the final game on Thursday.