O'Driscoll capped his 141st and final appearance before international retirement by winning the title for the second time in his career. His team rebuffed a late French onslaught to finish top of the table for the first time since 2009 after claiming only their second Paris win in 42 years on what was a day of drama for Sexton.
As well as scoring twice, the Racing Metro fly-half missed five points with the boot and was knocked out cold trying to tackle Mathieu Bastareaud.
O'Driscoll, who will continue to play at club level, said: "It feels great to be a two-time Six Nations winner. It's great to finish on a high in my last game in this magnificent jersey. When I do hang it up on the hook inside, it'll be with very fond memories.
"I'm absolutely delighted but I know now why I'm packing it in: 80 minutes is a long bloody time at international level, particularly with guys like Mathieu Bastereaud running at you - it's no fun."
Ireland captain Paul O'Connell added: "It's fantastic for Ireland but also for Brian and his family. To be part of the team that laid the platform for him to have a great finish to his career is great for everyone involved."
Ireland were forced to weather a first-quarter storm as France responded to their critics. Maxime Machenaud put the home side ahead with two penalties before Ireland hit back with the first of Sexton's tries.
Chris Henry's cute off-load outfoxed the home defence after smart build-up play and Sexton caught sight of the half-gap to cut back inside and over the whitewash, although he missed what should have been a straightforward conversion. Ireland quickly doubled their try count when Conor Murray blasted through a gap and sent Andrew Trimble under the sticks after a move set in motion by O'Driscoll's straight and true drive to the gain line, with Sexton this time adding the extras.
France replied with a touchdown of their own when Remi Tales chipped to the wing, Yoann Huget tapped inside at full leap to give Brice Dulin an easy run home and Machenaud's expert touchline conversion wrestled France a 13-12 lead. Ireland had a chance to retake the lead before the interval but Sexton missed a penalty.
He started the second half with another error, his risky chip easily dealt with by Gael Fickou, setting France away on a trademark counter-attack.
However, Rob Kearney swept up Huget's chip in behind, then O'Connell won a vital ruck turnover penalty. Rob Kearney again cleaned up the mess, latching on to a deft boot through the line from the French to clear, after Mike Ross's knock-on.
Sexton quickly recovered to bag his second try. When Huget failed to hold Bastareaud's pass, it was Ireland launching the counter, through Rob Kearney. Trimble cut away down the right, feeding O'Driscoll, who had the presence of mind to recycle deep in the France 22. O'Connell carried on, and Murray sent Sexton under the posts.
Sexton converted and then added a penalty to put Ireland 22-13 ahead. Following a penalty line-out in Ireland's 22, Dimitri Szarzewski added a second try for the French, although replays suggested the hooker fumbled in the act of scoring. Machenaud landed the conversion to cut Ireland's lead to just two points.
Sexton was stretchered off after being knocked unconscious trying to fell Bastareaud before Jean-Marc Doussain sent wide a penalty that would have put France in front. Damien Chouly thought he had stolen the game when he nipped into the right corner, but Vincent Debaty's pass was rightly ruled forward and the title was heading to Dublin.
France: Dulin, Huget, Bastareaud, Fickou, Medard, Tales, Machenaud, Domingo, Szarzewski, Mas, Pape, Maestri, Picamoles, Lapandry, Chouly.
Replacements: Mermoz for Fickou (75), Doussain for Machenaud (66), Debaty for Domingo (41), Guirado for Szarzewski (68), Flanquart for Maestri (53), Vahaamahina for Picamoles (66), Lauret for Lapandry (75). Not Used: Slimani.
Ireland: R Kearney, Trimble, O'Driscoll, D'Arcy, D Kearney, Sexton, Murray, Healy, Best, Ross, Toner, O'Connell, O'Mahony, Henry, Heaslip. Replacements: McFadden for D'Arcy (66), Madigan for Sexton (68), Reddan for Murray (63), McGrath for Healy (70), Cronin for Best (70), Moore for Ross (63), Henderson for O'Mahony (63). Not Used: Murphy.
Referee: Steve Walsh (Australia).