The Boys In Green had got the better of the rain affected two-day game, which was eventually abandoned with Ireland on top.
They claimed the first innings points (2) from the rain-interrupted draw as YMCA all-rounder Mitchell Thompson finished 67 not out and Northern Knights and Rush wicket-keeper Neil Rock scored 80 as Ireland made 221-5 in reply to the Scots 164 all out.
They each hit 11 fours, and Thompson also cleared the ropes once in a stand of 127 for the fourth wicket.
Alex Stiles and Marcus Poskitt both scored 27.
In the Scottish innings, Bready’s Gregory McFaul claimed 4 for 40 as Scotland slumped to 37 for 7, with JJ Garth taking 3 for 31 and Gavin Hoey 2-40.
Liam Naylor (62) and Tom Bradburn (41) - son of Scotland Head Coach Grant - shared an 8th wicket partnership of exactly 100 to rescue their side from disaster.
Tuesday's 50-over contest was a high scoring encounter, as the Irish racked up 267 for 8.
Oliver Metcalfe hit 7 fours in a quickfire 40, sharing an opening stand of 72 in 12 overs with Marcus Poskitt (25).
However, both they, Alex Stiles and Mitchell Thompson fell in quick succession as Ireland lost four wickets to collapse to 85 for 4.
Max Burton (39) and Neil Rock (45) counter-attacked, with Burton clubbing 3 sixes and 4 fours.
James Hunter kept the attack going as he top-scored with 74 (8 fours, 2 sixes), adding 60 with JJ Garth (17).
Euan MacBeth (3-39) and Tom Bradburn (2-61) were best with the ball for the hosts.
Scotland's chase started strongly with Tom Mackintosh (56), Jasper Davidson (51) and Angus Guy all among the runs.
Mitchell Thompson (4-51) and JJ Garth (3-26) put the Irish well in control, and despite a late rally from Liam Naylor (44*), they hung on to secure the win that clinched the series.
The teams meet again on Thursday in a T20 game which concludes the series.