Ex-captain Brendan Taylor made only seven in his final international game while Craig Ervine’s 57 helped the tourists to a modest 131 all out.
More rain left Ireland facing an adjusted target of 118 from 32 overs under the Duckworth-Lewis-Stern method. Paul Stirling (43) and Andrew Balbirnie (34) helped them cruise to victory.
Zimbabwe won the opener at Stormont but the second game was washed out and rain would again impact the final encounter between the sides.
The match was reduced to 42 overs and then 38 but Ireland would only need 34 to dismiss Zimbabwe with opener Taylor bringing a 17-year international career to an end on his 284th appearance.
The victory is just the fourth for Ireland in their 15 World Cup Super League games.
Chief scores
Zimbabwe: 131 in 34 overs (C. Ervine 57, A. McBrine 3/26, J. Little 3/33)
Ireland: 118/3 in 22.2 overs (P. Stirling 43, A. Balbirnie 34). (BBC)