The unseeded 22-year-old, who beat Britain's Andy Murray in round one, was coolness personified and some precise volleying created a break in game two.
A love game secured the next set and Nadal found no answer as the awesome Tsonga sealed victory in 117 minutes.
Novak Djokovic and Roger Federer play the second semi-final on Friday.
Tsonga, world ranked 38 and competing in only his fifth Grand Slam, admitted that even he had been surprised by his phenomenal performance.
"It is just amazing, unbelievable, nothing could stop me today," he said.
"I tried to hit everything and everything went in, so what can I say? "My family said it is like a dream for them, everybody in France is happy for me. I will try to do my best for the final."
An inspirational Tsonga was in such complete command that Nadal did not not have a break point until the second game of the third set.
The Spaniard, who had not previously dropped a set in the tournament had two break point chances in that game, but Tsonga somehow managed to return a fierce groundstoke aimed straight at his body from close range.
Nadal spurned another rare chance, while Tsonga was briefly infuriated when an ace had to be replayed having been overruled by an official, only for replays to prove the ball had been inside the line.
It did not prove significant as Tsonga then sent down successive aces and quickly held serve.
That proved to be Nadal's final hope and after sending a cross-court attempt wide of the line he lost his serve to trail 2-1 and was soon shaking his head in disbelief beneath his towel at the changeover.
Tsonga broke again and sealed an epic victory with an ace, a match which saw him produce 49 winners to 13 from the Spaniard.