After surviving a first half of almost total French domination, lone striker James McFadden scored a glorious 30-yard drive in the 63rd minute to give Scotland all three points.
Alex McLeish’s side are top of Group B, having taken six points from the French and with two of their last three games at Hampden Park.
Italy moved in to second place with a win in Ukraine but the night belonged to the Scots, who caused a massive shock in Paris — and one which looked so unlikely for most of the match.
Manager Alex McLeish said the victory was Scotland's best result in modern times.
And when asked if Scotland will qualify for the finals, he replied: “We can - we’ll leave it at that.”
McLeish said: “We got the break, we didn’t have too many attacks and we did say we would have to weather the storm at times.”
McLeish described McFadden’s goal as “inspirational”.
In the 26th minute Stephen Pearson replaced Fletcher, who appeared to have injured himself in the tackle on the Chelsea midfielder.
Just after the half-hour mark Ribery’s goalbound drive from the edge of the box deflected off Alexander but Makelele’s corner was easily gathered by Gordon.
Towards the end of the half Scotland enjoyed a brief spell of possession but could not make any impact on the French goal although McFadden drew a save from Landreau after good work on the bye-line.
When referee Konrad Plautz blew to restart the game there was no surprise when the Scots filed back and within two minutes Ribery had fired in another effort, but again the Bayern Munich player’s effort was wide.
Despite their domination, the French were almost as impotent as Scotland, especially with regards to their final ball in to Gordon’s penalty area.
But in the 55th minute Anelka presented Ribery with the best chance of the game with a clever dink just inside the Scotland penalty area.
Ribery’s left-footed strike from 12 yards was parried by Gordon and the France midfielder blasted the rebound high over the bar.
Seconds later the Sunderland goalkeeper pulled off another great save, tipping Anelka’s shot from 12 yards over the bar, the Scots again surviving the resultant corner.
Suddenly the tempo had lifted and Hartley was then rightly booked for scything down Ribery on the touchline.
Then in the 63rd minute Scotland turned the game on its head with the game’s decisive moment.
The ball broke to McFadden at least 30 yards from goal and, out of the blue, the Everton striker drove a glorious shot in the top corner.
Parc des Princes was stunned — apart from the section housing the Tartan Army.
The French supporters could hardly take in the scoreline as their favourites pounded the Scottish penalty area in search of the equaliser.
The Scots fans dared to look for another goal.
However, the tension during the final moments was almost unbearable but somehow Scotland held on to start a massive party in Paris.
Landreau, Lassana Diarra, Thuram, Escude, Abidal (Benzema 77), Ribery, Vieira (Nasri 69), Makelele, Malouda, Trezeguet, Anelka.
Gordon, Hutton, McManus, Weir, Alexander, McCulloch, Ferguson, Fletcher (Pearson 26), Brown, Hartley, McFadden (O’Connor 76).
Konrad Plautz (Austria).