The world number one looked utterly convincing as he romped through the opening set, losing just one game, but Tsonga produced some virtuoso tennis to take the next two sets in dramatic fashion before going on to stand on the brink of causing a major upset.
Tsonga had four match points in the fourth set, but Djokovic showed remarkable resilience in pulling through and taking it on a tie-break before coasting through the decider to set up a semi-final clash with third seed Roger Federer.
The pair came into the encounter with a 5-5 head-to-head record - Tsonga took five of their first seven but came up short at Wimbledon and the Rogers Cup last year and Rome, at the quarter-final stage, three weeks ago – and it always looked destined to be a classic.
Djokovic broke in the fourth game of the opening set as Tsonga produced an alarmingly sluggish service game with a double fault and two unforced errors handing the top seed control.
The Frenchman was unable to get going at all in the opening set as he saw his serve repeatedly attacked with Djokovic openly surprised at the ease with which he was able to assert his authority.
Tsonga folded tamely as he lost his serve again in losing the set, and it was a subdued atmosphere on a previously expectant Court Philippe Chatrier as Djokovic coasted.
An immediate break at the start of the second set compounded Tsonga’s misery, and ironic cheers greeted his belated hold in the third game as he established himself in unconvincing fashion.
But the match began to turn around as Tsonga, buoyed by growing support on Chatrier, levelled at 4-4 with an inspired assault on the Djokovic serve as the Frenchman began to thrive.
Indeed, Tsonga was eventually settling into a good rhythm on serve as he and Djokovic exchanged thrilling games with the second set finely poised.
A remarkable resurgence was complete as Tsonga pounced in opportunist fashion to break serve at 6-5, and level the match at one set-all, with Djokovic left utterly shell-shocked in the face of a barrage of pressure.
The top seed’s emotions were becoming increasingly frayed as he shouted angrily up at his box after losing the opening game of the third set, and he was pushed to his limit as he managed to hold after a seemingly interminable deuce.
But Tsonga had a costly aberration on serve in the third game of the set as he slipped to 0-40 and proceeded to plant a tame volley into the net to fall behind with Djokovic incredibly fired up.
The Frenchman was undeterred, however, and restored parity with a virtuoso performance on return as he pounded a series of breathtaking groundstrokes from the back of the court, and the third set was back level.
Neither player was able to seize the initiative as the set looked to be heading towards a tie-break, but there was a twist once more as Tsonga broke serve for a second time to take it 7-5 as Djokovic was left shell-shocked and suddenly behind in the match.
It was a cagey start to the fourth set as both players traded confident and assured service holds, but Tsonga’s serve came under tremendous pressure in the fifth game as he fended off three break points.
Djokovic was left to bemoan his profligacy as Tsonga held serve, and both players worked tirelessly around the court as extremely tough holds were exchanged.
Tsonga forced the issue in the 10th game of the set as he forced two match points at 15-40, but a fearsome response from Djokovic saw the Serb save both as he proceeded to rescue two more with hugely impressive mental resolve in a pulsating game.
The fourth set, perhaps inevitably, had to be decided on a tie-break and Tsonga immediately took control, bludgeoning two forehand winners before Djokovic responded in style.
Djokovic forced two set points at 6-4 in the breaker, but had to push again from 6-6 after his opponent hit back though the Serb’s perseverance and relentless pressure eventually saw him take the set to take the match into a decider.
Tsonga cut a weary, despondent figure at the start of the fifth set and wilted under a barrage of powerful groundstrokes from the incessant Djokovic to concede an early break of serve.
The world number one managed to muster more energy and intensity in the final set with both men clearly exhausted, and the Serb found the strength to break twice and serve out for the match.
Tsonga acknowledged the Parisian crowd as they gave the pair a standing ovation, but he was left distraught after a brave showing in defeat, while Djokovic proved once again why he is the world number one. A semi-final clash with Federer awaits.