Hamilton made a 150-ball 115 and knitted an impressive 122-run stand with Colin Smith (59) for third-wicket as Scots overhauled the Irish total of 210 with fine wickets in hand and 15 balls to spare.
Colin Smith had a good outing behind the stumps as well, taking five catches in an excellent all-round display.
Hamilton, a former England bowling all-rounder, blasted the Irish bowlers to all parts of the ground, bringing up his ton in 136 balls. He found good support in the debutant Qasim Sheikh (23) and Smith.
White captured two late wickets to finish with 2/17, while Kyle McCallan (1/34) did well to keep the Scots scoring rate to an acceptable level during the middle stages of the innings.
Earlier, Ireland wilted under the fierce bowling of Nel to be 4/66, losing as many as four wickets for just 65 in the 20th over with only Wilson (39) showing any resistance.
White (34) and Ryan Haire (54) put on a solid partnership worth 65 as Ireland crawled to 153/7 before Thinus Fourie (19 not out) and McCallan (39) took Eire past 200.
Nel was the pick of the Scots' bowlers with 4-25, while John Blain and Gordon Goudie took two wickets each.
Ireland 210/8 in 50 (Haire 54, McCallan 39, Wilson 39, Andrew White 34; Dewald Nel 4/25, Blain 2/29, Goudie 2/43) lost to Scotland 211/5 in 47.3 (Gavin Hamilton 115, Smith 59, Sheikh 23; Andy White 2/17, McCallan 1/34).