Ireland become first team to qualify for the 2015 Cricket World Cup
Ed Joyce's unbeaten 96 had paved the way for Ireland to post a testing target but the Dutch, second in the qualification table, remained up with the rate until a late clutch of wickets.
Mooney then looked set to be the match winner when the first three balls of his final over went un-hit and Edgar Schiferli was run out attempting to steal a single.
But after Mooney's penultimate ball was lofted to the mid-off rope he produced a slow bouncer that Rippon dispatched to secure a tie that boosted Holland's own qualification bid.
Joyce was the cornerstone of Ireland's innings as he fell just short of a second one-day international century in Irish colours - after his first against Pakistan in May.
Holland set about chasing down the target with all of their top-order getting starts.
But after Paul Stirling's part-time spin removed openers Stephan Myburgh and Eric Szwarczynski, Kevin O'Brien (three for 52) picked up Warren Barresi and then, most importantly, Tom Cooper late on.
Cooper's dismissal left the Dutch needing 17 from the final 13 balls and when Alex Cusack's penultimate over cost just three, 13 were needed from Mooney's last.
The all-rounder looked set to seal the result when Holland failed to score off the first three balls only to lose his composure at the end.