After starting the final day on 199-6, Ireland were bowled out for 230 to leave Hong Kong needing 310 to win.
Nizakat Khan's superb 123 held up Ireland as he shared a ninth-wicket stand of 61 with Nadeem Ahmed.
However, with the score on 239, Peter Chase trapped Ahmed and Khan was then dismissed by Tim Murtagh.
Middlesex seamer Murtagh was the pick of Ireland's bowlers on the final day as his closing dismissal, with Ed Joyce taking a simple catch, brought impressive figures of 4-29.
George Dockrell and Kevin O'Brien chipped in with two wickets apiece but the Ireland attack laboured for most of the final afternoon as Khan and Ahmed looked comfortable during their 61-run partnership.
Earlier, a quick victory looked on the cards as Murtagh's first two wickets and O'Brien's dismissals left Hong Kong on 114-5 before they slipped 147-7.
Ireland were able to add only 31 runs for the loss of their final four wickets at the start of the day as O'Brien finished unbeaten on 16.
The victory maintained Ireland's winning run in the competition as they moved back to the top of the eight-team table.
After four successive wins, Ireland lead Afghanistan by 19 points, with the two sides meeting in the next fixture in India next March.
The winners of the eight-nation competition will play the bottom-ranked Test nation in 2018 for the right to earn four years of Test cricket status.
Ireland remain on course to battle for a place in Test cricket in 2018 after beating Hong Kong by 70 runs in the Intercontinental Cup game at Stormont.