The Serbian star, who followed up his fourth Australian Open title in January with an ATP triumph in Dubai, took just 54 minutes to beat eighth-seeded Tsonga 6-3, 6-1.
He awaits the winner of the day’s other quarter-final between world No. 3 Andy Murray and seventh-seeded Argentinian Juan Martin del Potro.
Murray is playing his first tournament since falling to Djokovic in a gritty four-set final at the Australian Open.
His run in Melbourne was preceded by a title in Brisbane as the Scot built on a stellar 2012 season that included Olympic singles gold in London and a US Open triumph.
If he can make it to the final here, he will overtake Roger Federer for No. 2 in the world rankings, after the defending champion was ousted in the quarter-finals on Thursday by a resurgent Rafael Nadal.
Whoever emerged from the Murray-del Potro match, however, faced a daunting semi-final against Djokovic.
Djokovic didn’t didn’t drop a point in four service games in the second set against Tsonga.
No sooner had the world’s top player given himself triple match point with a pair of aces and the demoralized Frenchman casually knocked a backhand wide.
“I thought Jo didn’t play his best — his serve wasn’t going well and that made life easier on court,” Djokovic said, but added that he couldn’t concern himself with his opponent’s struggles.
“I really didn’t care about how my opponent felt,” he said. “I just tried to focus on the job I need to do, and my performance was really good.
“I served really well and used the shots around the court well, and that’s what matters for me.”
Tsonga double faulted to give Djokovic the first break chance of the match in the fifth game. In the next rally, Djokovic unleashed a low backhand that Tsonga could only smack into the net.
But Tsonga said his own errors were a bigger problem than anything Djokovic did.
“I did a lot of mistakes,” Tsonga said. “It was tough for me to keep the ball in the court. Not because he put me a lot of pressure … it was a day for me without sensation. Everything I tried to do, I missed it.”
Three of Tsonga’s four double faults came in the second set, including two to give Djokovic a triple break point in the second game.
The Frenchman saved two before Djokovic claimed the break and virtually sealed Tsonga’s fate.
Tsonga served up another double on break point in the sixth game to leave Djokovic to serve for the match at 5-1.