Jonathan Sexton was the match winner once again for Joe Schmidt's men, slotting five successful penalties from as many attempts as Ireland earned back-to-back victories over France for the first time since 2000-2001.
Four pinpoint strikes from the returning Jonathan Sexton, who was back at out-half after his 12-week concussion lay-off, established a 12-6 lead for Ireland at half-time.
Try-scoring chances were few and far between for both sides and a clash of heads between Sexton and bulldozing France centre Mathieu Bastareaud, early in the second half, forced both players off for a short spell. In Sexton's absence, replacement Ian Madigan landed a penalty.
Following French lock Pascal Pape's yellow card for kneeing Jamie Heaslip in the back, Ireland's best try-scoring opportunity was lost when Sexton's short pass was too strong for Jared Payne with Rob Kearney and Simon Zebo lurking out wide.
Rory Best was then sin-binned for sticking a leg out at a ruck, however the usually reliable Camille Lopez missed the penalty and Sexton followed up with his best kick of the night as he punished Damien Chouly for a lineout infringement.
Trailing 18-6, France lifted their game on the back of Morgan Parra's introduction and the carrying of their bulky forward replacements, including Romain Taofifenua who finished off an overlap in the 71st minute for the game's only try.
Lopez sent the conversion wide from the left and with the fit-again Cian Healy and Iain Henderson making a physical impact off the bench, Ireland defended with impressive discipline late on to make it two wins out of two in the 2015 RBS 6 Nations.
Joe Schmidt's charges have now won seven successive games at the Aviva Stadium where they will host fellow unbeaten team England in a mouth-watering top of the table clash in two weeks' time.
Ireland captain Paul O'Connell said afterwards: "France are a good side, a big side, and we're very relieved to get that win. The pressure told when they scored that try but we defended brilliantly. England in a couple of weeks is going to be the kind of challenge many of us have never faced before and we can't wait."