Ashraf returned figures of three for 29 and along with seamer Dawlat Zadran (two for 39) was the pick of the bowlers as Afghanistan recorded their biggest ever 50-over victory by runs.
Having been sent in to bat, Afghanistan posted a par-score of 259 as they were bowled out in the final over, wicketkeeper Shafiqullah Shafiq top-scoring with 56.
Seamer Donald Tiripano was the pick of the Zimbabwe bowlers as he recorded career-best figures of five for 63.
Zimbabwe were in early trouble in their reply and never recovered from a position of 26 for six, despite a rally from debutant wicketkeeper Richmond Mutumbami, who struck 64 from 75 balls to play a lone hand for the hosts.
Afghanistan lost the opening two games of the series, but rallied in the final two matches to end a hugely satisfying tour for the Asian side.
Brief scores:
Afghanistan: 259 all out in 49.1 overs (Shafiqullah Shafiq 56; D. Tiripano 5-63)
Zimbabwe: 159 all out in 38 overs (R Mutumbami 64; Sharafuddin Ashraf 3-29)
Image: Sharafuddin Ashraf
Photograph: Getty Images