The Irish have silverware regardless, their sixth Triple Crown in the Six Nations era, since 2000. But it was their first trophy won in front of their home crowd in 18 years.
That made their seventh straight home win over Scotland a little tastier.
But it didn't come easy in a messy match at Lansdowne Road.
Scotland was disruptive and competitive, giving a better effort than it did in beating Italy in Rome last weekend.
But Ireland's superior power in the pack was decisive, with three of their tries to the forwards coming off rucks or mauls. The bonus fourth in the last minute wasn't pretty either, as replacement scrumhalf Conor Murray took an offload from wing James Lowe and crashed through three Scots to score.
The first try was to busy hooker Dan Sheehan, who broke off a rolling maul to cross in the 17th minute. Prop Cian Healy went over in the 28th with a helpful push from Sheehan and locks Tadhg Beirne and Iain Henderson.
Scotland looked contained, but reminded the Irish not to drop their guard just before halftime when prop Pierre Schoeman, with three Irish on his back, reached out to plug the ball on the try-line.
Scotland, behind 14-5 at halftime, should have had the next try in the new half but captain Stuart Hogg wasted a four-on-one chance by going for the line himself, and being tackled out in the corner by Hugo Keenan.
After more than half an hour of near-misses and Scotland resistance, Ireland finally posted a third try when flanker Josh van der Flier, the only Irishman to play every minute of the campaign, blew through a channel of Scots to score.
Sexton added his third straight conversion but missed the last chance.
Scotland's third defeat in five matches condemned it to fourth place for a third straight year.