Ireland won the tense Pool B match by five runs after setting Zimbabwe a huge 332-run total to chase and stay in the tournament at Hobart's Bellerive Oval.
With Zimbabwe needing 32 to win off 20 balls and with four wickets left, Sean Williams, on 96, launched a huge hook off Kevin O'Brien towards deep midwicket where Mooney reached high to grab the ball.
As the decision was examined, Williams left the Bellerive Oval pitch and the catch stood.
"You've got to take his (Mooney's) word for it. They zoomed in, and I thought it was pretty clear. But you've got to take the fielder's word," said Taylor who hit a blistering 121 with 11 fours and four sixes as his team chased what would have been a record score.
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The result meant that Zimbabwe, with four defeats and one win, have no hope of making the quarter-finals while Ireland are still in contention after their third win and with two more group games to play this week.