By the time winger Blair Kinghorn claimed Scotland's sole try, Ireland had three, two to wing Jacob Stockdale.
It was a nervy affair for Ireland, having lost a 12 point half-time lead in the second half.
Scotland showed glimpses of the form that saw them beat England in the previous round of matches but left too many points out on the field through bungled passing.
A much-prized third Six Nations trophy win in five years for Ireland, adding to the 2014 and 2015 triumphs under head coach Joe Schmidt, was confirmed a week early following England's 22-16 loss to France tonight.
"We are three or four years behind Ireland in terms of what they've done and achieved over the last few years", Scotland coach Gregor Townsend said. "Any team that is developing as we are, you go through these tough periods, when the game doesn't love you", he said.
Blair Kinghorn's try did narrow the lead to 21-8 in the 51st minute, but Ireland were simply more clinical, and there was a sense of elation when a lineout move in the corner resulted in Cronin, nearly on his knees, going over.
Wales gave away just two penalties against England at Twickenham, but conceded nine in the Aviva stadium.
Schmidt took over a demoralised Irish side after the 2013 Six Nations but then guided the Irish to back to back titles in 2014/15.
Tadhg Furlong returns to the Ireland team today Credit Brian Lawless PA
Scotland upended England last time out but that was at Murrayfield.
It was a 20-point result in a one-score game because Scotland probably butchered a couple of really good chances.
"We'll have to look how we can be more clinical", stand-in captain Farrell said.
"Over the next 18 months before we play Ireland in the World Cup, we have to make sure we are improving, and we are a better team for the next Six Nations and a better team at the  World Cup".
France has traditionally capitalised following a British and Irish Lions tour, as the home nations' best players battle fatigue after a long season.
But for the trip to Paris Jones has kept faith with Courtney Lawes, Chris Robshaw and Nathan Hughes in the back row. Against the run of play, the Scots took the first points from a Greig Laidlaw penalty. But there was a lot of energy and a lot of will from the players.
It was France's first win over England in four years.
"We haven't talked about the bigger picture of the championship at all - just putting in a good performance against Ireland", said the defence chief. Expect fireworks if they are still in with a sniff of the title and know exactly what they have to do.
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