Returning flyhalf Johnny Sexton outkicked opposite number Camille Lopez to give Ireland a six-point halftime advantage that they stretched in the second period before a Romain Taofifenua try meant the hosts had to survive a late onslaught.
The victory put Ireland level on points at the top of the table with England.
"Irish teams don't beat France all that regularly so to do it back to back...is fantastic," captain Paul O'Connell told national broadcaster RTE.
"We never really took control for long periods. We took control for short periods and you probably need to back it up to dominate and I don't think we really did that."
Ireland's intent was clear from the start. They were prepared to run with the ball more than in recent outings while looking to neutralise the French with intense defending that is becoming a trademark under coach Joe Schmidt.
Mathieu Bastareaud, the player Schmidt reckoned would require three of his men to take down, was turned over twice in the first 10 minutes while Robbie Henshaw got into opposite number Wesley Fofana's face straight from the first whistle.
Sexton, back after an enforced 12-week layoff after suffering four concussions in a year, kicked Ireland into a 6-3 lead with two penalties either side of a strike by Lopez.
The home team then added two more Sexton penalties, again either side of one from Lopez.
BLOODIED HEADS
After his series of concussions began in a clash with Bastareaud in Paris last year, Sexton thundered into the big centre again early in the second half and both went off with bloodied heads.
In Sexton's absence, temporary replacement Ian Madigan nudged Ireland nine points in front before visiting coach Philippe Saint-Andre brought on a new front row after 50 minutes.
However, Pascal Pape was then sent to the sinbin for kneeing Jamie Heaslip in the back, forcing the number eight to hobble off on his return from injury.
The hosts went for the kill but a rare misjudgement and poor pass from the returning Sexton let France off the hook.
Ireland hooker Rory Best joined Pape in the sinbin for a trip on Thierry Dusautoir before Lopez missed the resulting penalty.
Sexton made it five penalties from five with 12 minutes to go before France finally went over for a try after pulling Ireland's defence apart and another miss from Lopez kept the gap at seven points.
France pushed for an equalising converted touchdown but Ireland kept them out.
(Additional reporting by Conor Humphries, editing by Alan Baldwin)
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