Tries by Dan Sheehan and Andrew Porter got the Irish over the line as the hosts were thwarted time and again by a magnificent Scottish defence.
It's a sixth title for Ireland in the Six Nations era as they retain their crown, with wins over France, Italy, Wales and the Scots.
Scotland opened the scoring in the eighth minute, Finn Russell slotting over a penalty to bring up a half-century of points in this campaign after James Lowe had been penalised.
However, the Scots gave away a soft try as hooker George Turner overthrew and it was picked off by Dan Sheehan who had the simplest of tasks to touch down - his fifth try of the tournament.
Jack Crowley converted from wide out on the right for 7-3.
Ireland's ill-discipline has been a glaring weakness in the championship and Russell landed a second penalty due to another Irish infringement in the 18th minute.
Neither side could impose themselves on the game as defences held firm with the Irish resorting to a long-range penalty attempt, instead of kicking to the corner, to try and get some breathing space.
However, Crowley dragged his effort wide and the clock wound down to leave the match very much in the balance at the end of a scrappy first-half.
The Irish, though, started the second period in lively fashion and Crowley landed a penalty after some excellent attacking play.
Russell's ability to make schoolboy errors then handed the Irish the initiative as he put the ball out directly from the kick-off.
The Irish turned on the pressure as the Scots defence wilted but Tadhg Furlong was denied a try as he was judged to have knocked on as he went to touch the ball down.
The Irish pressed but Calvin Nash was guilty of failing to pass as he closed on the line and the outstanding Scottish flanker Andy Christie forced a turnover.
The Scottish defence was magnificent as the Irish camped on their line and although they conceded penalties somehow they kept the hosts out.
They also managed to force errors with the normally reliable Garry Ringrose, making his first appearance of the tournament, showing his rustiness as he knocked on with the line beckoning.
Ringrose, though, redeemed himself with a superb solo run down the wing which gave the Irish a great position but again they were denied a try as Robbie Henshaw was held up.
However, referee Matthew Carley had lost patience with the Scots conceding penalties and sin-binned Ewan Ashman whilst awarding the Irish another penalty.
This time with a man advantage the hosts made no mistake as Andrew Porter went over and Crowley converted to stretch Ireland's lead to 17-6.
The Scots hit straight back after Harry Byrne was sin-binned, Huw Jones breaking through and touching down under the posts.
The Irish managed to see out the final minutes of the game, allowing their signature tune Zombie by The Cranberries be played at full volume once Carley blew the final whistle.