Ireland boosted their Six Nations title hopes and ended France's run of 14 straight wins as they battled to a pulsating bonus-point win in Dublin.
Ireland scored three first-half tries with Hugo Keenan, James Lowe and Andrew Porter all crossing.
Damian Penaud's brilliant counter-attacking try and three Thomas Ramos penalties kept France in touch.
Ramos cancelled out Ross Byrne's penalty with a drop-goal, but Garry Ringrose's try secured Ireland's win.
The victory further underlines Ireland's status as the world's number one side and gives Andy Farrell's side a national record 13th straight home win, while ending France's dream of a second successive Grand Slam.
Having taken bonus-point wins over Wales and France, Ireland will next face Italy in Rome on 25 February with France hosting Scotland a day later.
Title favourites live up to billing in breathless first half
Saturday's match had been billed as a titanic showdown between the championship favourites and it comfortably met the hype as the world's top two sides produced an electrifying first-half spectacle.
While France took an early lead through Ramos' fifth-minute penalty, Ireland immediately set about regaining control and, while Andrew Porter was denied a try in the hosts' opening attack, Finlay Bealham's sleight of hand sent Keenan scything through before crashing over for a well-worked score.
However, after a second Ramos penalty cut Ireland's lead to a single point, France ruthlessly exploited space in the home side's defence when Anthony Jelonch rampaged through Irish bodies and fed Penaud, who sprinted clear to finish off a stunning counter.
With most of the stadium still marvelling at Penaud's score, Ireland worked the ball out to Lowe who, despite Penaud's attempts to push him into touch, acrobatically managed to touch the ball down in the corner, with the try standing following a lengthy TMO review.
Sexton's failed conversion attempt meant Ireland trailed 13-12, but after Uini Atonio was yellow-carded for a high hit on Rob Herring, Porter marked his 50th cap by scoring Ireland's third try before Sexton's penalty put the hosts six points clear at the end of a breathless opening 40 minutes.
Ireland hold on before Ringrose settles classic
Following a thunderous first half, excitement turned to tension after the restart as the intensity dropped and France set about narrowing the deficit.
However, they failed to make inroads as Ramos missed a long-range kick at the posts before Stuart McCloskey eased the mounting pressure on the Irish defence by forcing a turnover close to the try-line.
After Ireland captain Johnny Sexton was forced off, his replacement Byrne's penalty split the posts to put Ireland nine clear before Ramos moved France to within six with a classy drop-goal.
While that put France within a converted try of victory, the away side's hopes of snatching a late victory were dashed when Ringrose somehow slipped past three French tacklers and touched down to give Ireland the bonus-point win after a championship encounter that will live long in the memory.
Farrell completes the set
Having been comfortably beaten in Paris last year, Farrell had urged his side to "take our game to them" and the players rose to the task with a performance that showcased Ireland's courage, skill and championship credentials.
It also completes the set for Farrell with the Englishman now having beaten all tier one nations during his three-and-a-half-year spell in charge of Ireland, after wins over southern hemisphere giants New Zealand, South Africa and Australia during a memorable 2022.
Farrell had lost all three previous meetings with France but Saturday's win will give Ireland the psychological advantage before a possible World Cup quarter-final meeting on French soil later this year.
That is further down the line, though. As for now, Ireland have kept alive their hopes of winning the Grand Slam for the fourth time in their history and will be considered heavy favourites to win a first title since 2018 as they prepare for matches in Italy and Scotland, before hosting England on 18 March.
Man of the match
It was another titanic display from Ireland number eight Caelan Doris, whose influence on Andy Farrell's team appears to be growing on a weekly basis.
'World-class performance' - what they said
Former Ireland head coach Eddie O'Sullivan on BBC Radio Ulster: "That was a world-class performance from Ireland. When you are number one in the world the expectation is to deliver a world-class performance and that was that. The number two side in the world couldn't break Ireland down there at times and gave up.
"Thomas Ramos going for the drop-kick was the white flag to say they weren't going to break Ireland down. Tactically Ireland were superb, especially in the final quarter."
Former Ireland flanker Chris Henry on BBC Radio Ulster: "Realistically, if this isn't for a Grand Slam now it is a failure. They need to go on and win this outright. They have the team on form to do this."
Line-ups
Ireland: Keenan; Hansen, Ringrose, McCloskey, Lowe; Sexton, Murray; Porter, Herring, Bealham, Beirne, Ryan, O'Mahony, Van der Flier, Doris.
Replacements: Kelleher, Kilcoyne, O'Toole, Henderson, Conan, Casey, Byrne, Aki.
France: Ramos; Penaud, Fickou, Moefana, Dumortier; Ntamack, Dupont; Baille, Marchand, Atonio, Flament, Willemse, Jelonch, Ollivon, Alldritt.
Replacements: Barlot, Wardi, Falatea, Taofifenua, Cros, Macalou, Couilloud, Jalibert.
Referee: Wayne Barnes (RFU)
Assistant referees: Matthew Carley (RFU) and Jordan Way (RA)
TMO: Brendon Pickerill (NZR)