The top-seeded Serb delivered a ruthless display against the eighth-seeded Frenchman at the Indian Wells Tennis Garden, breaking his error-prone opponent twice in each set and not dropping a single point on his own serve in the second set.
"I definitely feel very happy about this performance today," Australian Open champion Djokovic said after improving his record for the season to 17-0.
"I thought Jo didn't play his best. He made a lot of unforced errors and his serve wasn't going well and that made my life a lot easier on the court.
"I really didn't care about how my opponent felt. I just tried to focus on the job I need to do, and my performance was really good."
Djokovic, who needed only 54 minutes to seal victory, will next meet Juan Martin Del Potro of Argentina, who beat British world number three Andy Murray later in the day.
The Serbian world number one will be looking to extend his stellar form, having not been beaten since last October when he was defeated by big-serving American Sam Querrey in the second round of the ATP Masters 1000 event in Paris.
The first two quarter-finals were completed on Thursday, Rafa Nadal continuing his impressive comeback by thumping long-time rival Roger Federer 6-4 6-2 and Czech Tomas Berdych sweeping past big-serving South African Kevin Anderson 6-4 6-4.
Djokovic stormed through the opening set in half an hour after breaking Tsonga in the fifth game, when the Frenchman dumped a backhand volley into the net, and also in the ninth, when his opponent blasted a forehand wide.
Tsonga's troubles continued in the second game of the second set when he double-faulted to give Djokovic three break points at 0-40, saved two of them but then lost the game when he netted a forehand.
The Frenchman was also broken in the sixth after delivering his fourth double fault of the match and the Serb served out in style, consecutive aces putting him 40-0 up before Tsonga's fading challenge ended when he pushed a backhand long.
"I served really well and used the shots around the court well, and that's what matters for me," Djokovic told reporters after improving his overall record against Tsonga to 10-5.
"I was in the balance. I returned well when I needed to. He made a lot of unforced errors, which obviously helped me to get in front. When it was important, I didn't allow him to come back to the match.
"I didn't allow him to have an opportunity to believe that he can maybe have a break back and get back into the match," added the Serb, who won the Indian Wells title in 2008 and 2011.
Tsonga was a dejected figure after losing his eighth successive match to Djokovic.
"I did a lot of mistakes," the Frenchman said. "It was tough for me to keep the ball in the court, not because he put me under a lot of pressure.
"I don't know how to explain that, but it was a day for me without sensation. Everything I tried to do, I missed it."
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