Ireland posted their best ever ODI score of 331 for eight with Ed Joice scoring 112 and Andy Balbirnie 97 as the two batsmen shared a 138-run stand for the third wicket after they were invited to bat.
Zimbabwe put up a valiant fight through skipper Brendon Taylor, who smashed a fighting 121, and Sean Williams who played a superb knock of 96.
However, Zimbabwe fell short by five runs with Ireland paceman Alex Cusack taking the last two Zimbabwe wickets in the first three balls of the final overs to knock the Africans out of the tournament.
Ireland are placed fourth in Pool B with three wins and a defeat after four matches.
Zimbabwe were reeling at 74 for four and it was the pair of Taylor and Williams who brought them back with their 149-run stand for the fifth wicket.
Taylor was dismissed by Cusak in the 38th over but Williams kept his side in the hunt. But once Williams was scalped by Kevin O Brien in the last ball of the 47th over, Zimbabwe looked in struggle again.
Some gritty batting by Regis Chakbwa (17) and Tawanda Mupariwa (18) raised hopes as they needed only seven runs off the last over, but Cusack bowled Cjakabwa in the first ball
and then had Muprariwa caught by skipper William Porterfield to end the contest.
Zimbabwe's decision to put Ireland in after winning the toss backfired spectacularly as the European giant-killers rode on Joyce and Bilbirnie's knocks to better their previous best of 329, made against England in the 2011 edition.
Bilbirnie was unlucky to miss out on a hundred when he was run out by Zimbabwe's stand-in skipper Taylor in the 50th over while attempting a tough second run.

Zimbabwe -
Chamu Chibhabha, Sikandar Raza, Solomon Mire, Hamilton Masakadza, Taylor (captain), Sean Williams, Craig Ervine, Chakabva, Tawanda Mupariwa, Tinashe Panyangara, Tendai Chatara

Ireland - Porterfield (captain), Paul Stirling, Ed Joyce, Niall O'Brien, Andrew Balbirnie, Gary Wilson, Kevin O'Brien, John Mooney, Cusack, George Dockrell, Andy McBrine.

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