Sexton was the Irish hero at a packed Stade de France with with a dramatic drop goal from the halfway line three minutes after the final hooter.
It meant Brunel started his France reign with an agonising defeat after a stunning solo try from Teddy Thomas had looked set to pinch an unlikely victory.
France led 13-12 with the clock in the red and Ireland struggling to get out of their half.
But a Sexton chip gathered by Keith Earls got them into opposition territory and then the veteran No.10 landed the crucial kick from hand for a remarkable victory.
The exciting finale, however, was in stark contrast to what had come before.
For 72 minutes there was little in the way of thrilling or expansive rugby in a match dominated by the forwards and played almost entirely in the middle two-thirds.
Thomas gives France initiative
But flying wing Thomas set the Stade de France alight.
Wide on the right, and with little space to work with, he accelerated down the line and swerved infield before making a beeline for the posts as flailing green-shirted Irishman failed to get a hand on him.
Substitute fly-half Anthony Belleau kicked the conversion and just as they had done two years ago, France had turned around a six-point half-time deficit with a late try.
But unlike 2016, there was to be another twist in the tale.
Belleau missed a penalty with two minutes left, giving Ireland one more chance to push for a score.
They claimed the 22 drop out and initiated a long sequence of almost five minutes of possession that ended with Sexton's incredible kick. The 32-year-old kicked all of Ireland's points.
It was an all-round bad day for the French as teenage fly-half Mattheu Jalibert's surprise debut, already an unspectacular affair, ended after half an hour following a knee-to-knee collision with Bundee Aki.
The 19-year-old did little wrong, or right for that matter, during a turgid first 30 minutes of forward-dominated rugby arm-wrestle.
It had taken just three minutes for Ireland to get on the board through a Sexton penalty after France were penalised for offside.
Ireland's discipline was letting them down but France were unable to capitalise and consistently ran into an impenetrable green wall.
Sexton knocked over a second penalty as Ireland proved the more effective with their scraps of chances.
France got on the scoreboard through a Maxime Machenaud penalty four minutes before half-time as Ireland were penalised for holding on in the tackle, but Sebastien Vahaamahina shoulder charged Conor Murray just before the break and Sexton duly slotted over his third kick from the tee.
French in control at the interval
The half-time scoreline, 9-3, was the joint lowest between these two sides in a Six Nations match.
Yet two years ago, France scored a second half try to snatch a 10-9 win after trailing 9-3 at the break.
Sexton and Machenaud exchanged penalties before the Irish veteran surprisingly pulled a kick wide of the uprights leaving the visitors 12-6 ahead going into the final quarter.
France's indiscipline was costing them and after a rare foray into the Irish 22, Vahaamahina infringed again and Ireland could clear their lines.
Out of nowhere, though, Thomas gave the home fans hope of celebrating a famous victory.
The try changed everything and suddenly, with tails up, France were all over the Irish.
Belleau could have as good as killed the game but his missed penalty was all the sniff the Irish needed, and Sexton made him, Brunel and France pay dearly.