2005 Lions tourist Gordon D'Arcy sealed the win with a late try as he returned to the international scene after a year's absence through injury.
Lions skipper Brian O'Driscoll was also on the scoresheet, with No8 Jamie Heaslip the other Irish try scorer.
France led 7-3 courtesy of a 14th-minute Imanol Harinordoquy score but the Irish fought back to lead 13-10 at the half-time break.
They stretched that advantage to 20-10 through O'Driscoll's score early in the second period but France narrowed the gap to just two points courtesy of a Maxime Medard try and a second drop goal of the match from Lionel Beauxis.
D'Arcy's try with around a quarter of an hour remaining gave Ireland breathing space once more but a Beauxis penalty narrowed the gap to leave Irish supporters dreading the prospect of a repeat of the 2007 result between the two sides when France clinched victory with a late Vincent Clerc score.
Fellow Lion Ronan O'Gara eased those fears shortly afterwards, however, as his well-struck penalty pushed the hosts two scores clear.
O'Gara's effort proved to be the last score of a thrilling encounter, leaving the majority of the 82,000-strong crowd at Croke Park to return home happy.