After his triumphs in London, New York and Melbourne, the Serb is bidding to become just the third man to hold all four Grand Slam titles at the same time and the first in 43 years.
The win over Tsonga makes it 26 straight match victories in Grand Slam tennis for Djokovic, but seldom has he been run so ragged as he was at times by the powerful Frenchman, who had let slip four match points in the fourth set.
The defeat meant Tsonga's dream of becoming the first Frenchman to win at Roland Garros since Yannick Noah in 1983 had been cruelly shattered.
Djokovic's semi-final opponent on Friday will be third-seed Roger Federer who defeated Juan Martin del Potro of Argentina in five sets.
"He was the better player for most of the match and I was fortunate to come back from four match points down. It was an incredible match," said Djokovic.
Tsonga said: "I did what I said I would and gave everything. I came close and I would have loved to have won."
The anticipation was huge as the two players came out onto a Philippe Chatrier centre court which was packed and sun-splashed for the first time in three days.
But the home fans were soon stunned into a gloomy silence as the world number one immediately took control of the match.
He broke in the fourth and sixth games to pocket the first set in under 21 minutes with disquieting ease and then moved 2-0 up in the second as the sun clouded over and the cold, overcast conditions returned.
The French fans tried to rouse their man with a round of noise and that seemed to do Tsonga some good as he stopped the run of seven games against him with a steady service game.
Djokovic though was unperturbed as he moved 3-1 up with a big forehand down the line.
Tsonga was at least competitive now, going for his shots and making the top seed scurry from side to side.
The Frenchman had his first break point against the Djokovic serve at 3-4 down and he took it with a ripping backhand drive that the Serb could not retrieve.
The set seemed to be heading toward a tie-break but Djokovic suddenly found himself under big pressure on serve at 5-6 and 15-40 down.
He saved the two set points to get to deuce, but when a third came up he was put under pressure by the weight of Tsonga's shots and was eventually forced to hit long.
With the crowd now fully into it, Tsonga had another break point at the start of the third set but failed to take it and was immediately made to pay the price as Djokovic broke to 15 in the following game to go 2-1 up.
The top seed ws 40-15 up on serve in the followng game, but a rash of unforced errors allowed Tsonga to run off four points in a row to level at 2-2.
Djokovic was starting to look outgunned as he looked up for encouragement from his parents in the VIP box, but there was little respite out on the court as Tsonga continued to look the stronger.
The Frenchman came within two points of taking the set on the Djokovic serve in the 10th game, and then had to stave off two break points in the following.
Once again a tie-break loomed and once again Tsonga opened his shoulders to blast a way past the Djokovic defensive wall and give himself a two sets to one lead.
Tsonga needed medical treatment to a blister on a finger of his right hand at 2-1 up in the fourth set before the Serb levelled at 2-2.
Djokovic then had two break points to move ahead, but two big first serves from the Frenchman left him shaking his head.
Tsonga could taste victory and his hopes were boosted further when Djokovic jarred his knee stretching for a service return in the seventh game.
The Serb levelled at 4-4 and he had another break point in the next game only for Tsonga to send down an ace.
Tsonga had two match points in the following game only for Djokovic to hold firm. Two games later two more match points escaped the Frenchman setting up a tie-break.
Djokovic trailed 2-4 in that, but with Tsonga looking increasingly tight, the top seed clawed his way back and forced a fifth set on his third set point
The world number one seized the occasion to jump out into a 3-0 lead and he raced away to pull off a stunning victory.
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