The US Open champion next faces veteran three-time Grand Slam winner Stan Wawrinka, who is a wildcard entry in Beijing, or Russia's Roman Safiullin.
Sinner arrived in the Chinese capital fresh from winning in New York for his second major title, having triumphed at the Australian Open at the start of the year.
With victory also at the Cincinnati Masters before the US Open, Sinner faced Jarry in red-hot form and on an 11-match winning streak.
The two went toe to toe in the first set but it was the Chilean who got in front when he broke for a 4-3 lead when the world number one fired long.
Jarry consolidated without losing a point in the eighth game and after double-faulting on his first set point, sealed the set with his fifth ace of the match.
Going behind seemed to sting a re-energised Sinner into action.
The top seed raced into a 3-0 lead in the second set, eventually wrapping the set up after briefly threatening to blow his advantage.
Sinner tamed Jarry's big serve to start the deciding set and grab an early break, winning the game with a terrific crosscourt backhand.
Sinner broke again for 4-1 and was well on the way to an ultimately comfortable win.
His main rivals in the Chinese capital will be four-time major champion Carlos Alcaraz and the Russian duo of Daniil Medvedev and Andrey Rublev, the third and fourth seeds.
Novak Djokovic is not in Beijing, where a WTA 1000 event is also taking place at the same time.
