Andy Balbirnie was run out in the last over for 97, which came in 79 balls, as Ireland posted their highest score in one-day internationals to boost their chances of a third victory in four matches at the tournament.
Left-hander Joyce (112) edged his first delivery off Tinashe Panyangara but the ball fell just short of Hamilton Masakadza at second slip.
The 36-year-old, who hit nine fours and three sixes during his 103-ball knock, was also dropped on 34 and then after completing his third one-day international hundred.
Joyce and captain William Porterfield (29) added 63 for the second wicket as Ireland made a watchful start after being put in to bat on a sluggish pitch in Hobart, hosting its first match in the tournament.
The momentum picked up during an Irish third-wicket record 138-run stand between Joyce and Balbirnie as the duo set up a solid platform for the big total.
Joyce was finally caught by Craig Ervine, who dropped him in the previous over, at mid-wicket off Tendai Chatara.
Balbirnie and Kevin O'Brien (24), who was also dropped on five, then smashed the Zimbabwe bowlers around, adding 59 runs in 33 balls.
Balbirnie, 24, looked set for his maiden ODI hundred only to run himself out on the first ball of the final over trying to go for a second run to get back on strike. He hit seven fours and four sixes in his highest ODI score.
Seamer Chatara and left-arm spinner Sean Williams picked up three wickets each for Zimbabwe, who have won once in their four outings and need victory to have any realistic hope of making the last eight.
