The Serb, who will be supplanted as world number one by Rafael Nadal on Monday, showed no signs of the cold that bothered him in his first two rounds as he produced a brilliant display that lasted less than an hour.
He will next face Bulgarian Grigor Dimitrov, whose solid run at Bercy continued when he saw off Chile's Cristian Garin 6-2 7-5.
Djokovic, a 16-time grand slam champion, raced through the first set and came close to handing Greek seventh seed Tsitsipas a bagel as he set up three set points at 5-0.
French Open order of play, Day 1 - Zverev, Alcaraz and Sakkari in action
Tsitsipas saved them but then surrendered the set with some awful shots.
After securing an early break in the second set, Djokovic did not look back as he avenged his quarter-final loss to the Greek in the quarter-finals of the Shanghai Masters this year.
Grigor Dimitrov's solid run at the Paris Masters continued when the Bulgarian saw off Chile's Cristian Garin 6-2 7-5 to reach the semi-finals on Friday.

Novak Djokovic

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Dimitrov, who had been struggling since being beaten in the U.S. Open semi-final in September, overcame a second-set wobble to set up a meeting with either world number one Novak Djokovic or Greek seventh seed Stefanos Tsitsipas.
Dimitrov made a quick start as he broke Garin in his first service game. The Bulgarian bagged the opening set with another break in the eighth game as nerves got the better of Garin who was contesting his first Masters quarter-final.
Dimitrov moved 2-0 up in the second set but Garin hit back with his first break of the match to level for 2-2 and he stole the 28-year-old's serve again to lead 5-4.
Dimitrov, however, broke straight back and wrapped it up on Garin's serve on his first match point.

Paris Masters : Highlights Dimitrov v Garin

Image credit: Eurosport

Later on Friday, France's Gael Monfils will snatch the remaining ticket for the season-ending APT Finals if he beats Canadian Denis Shapovalov.
Should he fail, Italian Matteo Berrettini, who was eliminated in the second round here, will earn the spot for the Nov. 10-17 event at the O2 in London.
Rafael Nadal, who will take over as world number one on Monday, takes on local favourite Jo-Wilfried Tsonga in the last match of the day at Bercy.
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