Les Bleus, who had lost nine of their last 11 meetings against England in the Championship, prevailed through penalties by Maxime Machenaud (4) and Lionel Beauxis and a penalty try while their opponents scored two penalties and conversion by Owen Farrell, a penalty by Elliot Daly and a try by Jonny May.
After Sexton dragged a kickable penalty wide the next award in the Scotland 22 was kicked to the corner, to the approval of the home crowd, as Ireland sought the bonus-point try needed to heap the pressure on England in Paris.
The 109-cap front-rower conceded blaming their late arrival for last year's Scotland defeat was merely an excuse, and admitted that had proved a steep learning curve.
But after missing France's first two Six Nations matches this year - both lost - due to a ban for uttering a homophobic slur in a club game, his return has given the team a huge boost.
Now the shoe will be on the other foot, with England at home on the final day endeavouring to atone for two away defeats and in the process deny their visitors a Grand Slam on their home patch, as Ireland did to England in 2001, 2011 and a year ago.
England, on the other hand, were a metre from the French line on the last play of their game but coughed up the ball.
By the time new cap Blair Kinghorn claimed Scotland's sole try, Ireland had three, two to wing Jacob Stockdale.
Should Joe Schmidt's side win, they will complete only their second Grand Slam in the Six Nations era and third overall. We have to go away to work on it.
"No one can catch us which is great, as it's 19 out of 20 points", said Ireland coach Schmidt.
"We need to go to Twickenham and try to test that record out, I guess".
They will win the Grand Slam if they beat England next Saturday.
But Eddie Jones' team didn't play like a side needing to score four tries to force a championship decider in a Twickenham head-to-head next week.
France coach Jacques Brunel praised his team's defensive performance.
"Winning the championship is fantastic but if we were to lose next week I think it would take away somewhat from what we have achieved so far", added the 19-times capped global.
"We knew the physical challenge would be key and we controlled the ball and that upset England, they're not used to that. We defended well and we always went forward". "Many of these stemmed from the breakdown", Dallaglio wrote in his column for The Times.
"If they are free in that zone, it becomes complicated for their opponents".
"Declan said I was just as much a part of it as everyone else in 2009 when I was on the bibs".
That decision bore no fruit and Scotland punished their hosts with their first real foray into the Irish half after 12 minutes, when Greig Laidlaw knocked over from the tee for the first points of the match.