The victory gave Afghanistan a 3-2 series win after the two sides had shared the first four games at the Queen's Sports Club.
Chasing a 246-run winning target, Zimbabwe were skittled out for 172 in the 45th over despite Sean Williams making a fine 102 off 124 balls with three boundaries and four sixes.
Inzamamul Haq appointed Afghanistan coach
Fast bowler Dawlat Zadran finished with a career best 4-22 in his 10 overs.
Earlier, opener Noor Ali Zadran made 54 and Mohammad Nabi, who hit a maiden century in the second match of the series, chipped in with 53 as Afghanistan reached 245-9 in their 50 overs.
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