Ireland made early use of the breeze at their backs with two penalties from scrum-half Ian Porter, but Scotland engineered several scoring opportunities with only heroic Irish defence keeping them at bay.
Things then went from bad to worse for Scotland as they lost influential centre Stephen McColl and then had second row Neale Patrick stretchered off within minutes of each other before conceding the game's first try just before half-time when left-wing Chris Cochrane touched down after a Scotland kick was charged down.
Trailing 13-0, Scotland had a second-half mountain to climb and it only became steeper when outside centre Eoin O'Malley scored under the posts.
The Irish wingers had the final word as Kearney and Cochrane each claimed their second tries in the match.
Ireland coach Eric Elwood said: "It was a good result for us. Any time you put 39 points on an opponent, it's a good result. It's been a long, tough tournament for us but we set out to win our last three games and we've done that. We know the Scots quite well and they were ravaged by injuries which was tough for them. But we can only play what's in front of us."