Gibaud vs. Lazard, 1924
Well, this is a fairly famous game, which probably never took place.
From Tim Krabbe's site:
But nothing will prevent "Gibaud - Lazard, Paris 1924, 4 moves" being published as the shortest decisive "master game": 1.d4 Nf6 2.Nd2 e5 3.dxe5 Ng4 4.h3 Ne3 and White resigned. Almost everything is incorrect about that statement: it was not a master game, White was perhaps not poor Gibaud, it was not played in 1924, it was 5 instead of 4 moves - and even at 4 moves, it would have had to share honours with other games.
What is true is that in his autobiography, Lazard gave a friendly game "Amateur" - Lazard, played in Paris, "around 1922", which went 1.d4 d5 2.b3 Nf6 3.Nd2 e5 4.dxe5 Ng4 5.h3 Ne3 and White resigned. Here, 5.h3 is not as stupid a blunder as in the shorter version, because White could at least have hoped to gain a tempo after 5...Nxe5 6.Bb2. "Amateur" becoming Gibaud, and Gibaud the proverbial patzer, is not Lazard's fault; he mentioned "a very strong player whose talent is done no justice by this game."
In fact, Gibaud was champion of France no less than four times. He didn't like this 4-move game going around with his name attached. And when in 1937 the British magazine Chess published it as "the shortest tournament game ever played, from a Paris Championship", he protested his innocence.
In the next issue, Chess answered: "He never lost any tournament game in four moves. Searching his memory he recalls a skittles he once played against Lazard, a game of the most light-hearted variety, in which, his attention momentarily distracted by the arrival of his friend Muffang, he played a move which allowed a combination of this genre - but certainly not four moves after the commencement of the game. Rumour, he said, must have woven strange tales about this game."
Lazard was of master strength too, but he is better known as a composer of endgame studies and problems.