The championship is Ireland's third in five years.
But the bigger prize would be beating England next week for Ireland to earn only a third Grand Slam, beside those in 1948 and 2009.
"We're going to have to save the best for last, and that's what it's going to take to win everything next week," Ireland captain Rory Best said.
"Everyone knows the size of the challenge. They haven't lost at Twickenham under Eddie Jones."
With an awful record away from home, the Scots' own championship bid was almost inevitably squashed by an Irish side who own the visitors in Dublin, where Scotland have won only once in 20 years.
Scotland had their chances but wasn't as accurate, and butchered two tries, probably three.
By the time new cap Blair Kinghorn claimed Scotland's sole try, Ireland had three, two to wing Jacob Stockdale.
The bonus-point fourth try came with 11 minutes to go, when hooker Sean Cronin, only three minutes after replacing Best, dived over from the back of a rolling maul.
"We've a lot of big leaders," Best said.
"At times when we were under pressure today and they were trying to play chaotic rugby, we were able to get a breath back and get control through the spine of our team."
Scotland coach Gregor Townsend conceded the gulf between the two teams.
"We are three or four years behind Ireland in terms of what they've done and achieved over the last few years," he said.
"We need to make sure that when we have these experiences that are tough, it goes into our work to improve.
"We play Ireland next year in the Six Nations and we will play them in 18 months at the World Cup and we need to make sure we are a better team when we play them."
France 22 (Penalty try; Maxime Machenaud 4 penalties, Lionel Beauxis penalty), England 16 (Jonny May try; Owen Farrell conversion, 2 penalties, Elliot Daly penalty). HT: 9-9.
