Svitolina, chasing her sixth title of the season, survived three break points in third game of the opening set before breaking her opponent's serve to claim the set.
Zhu, currently ranked 115 in the world, struggled for rhythm as she committed 32 unforced errors during the match.
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She was often pushed further down the baseline by her Ukrainian opponent, who fired 19 winners to seal victory.
Last year's semi-finalist Svitolina will meet Wuhan Open runner-up Ashleigh Barty of Australia in the second round.
Poland's Agnieszka Radwanska began her title defence in Beijing with a convincing 7-5 6-3 win over Carina Witthoeft.
The 11th seed made a slow start but rediscovered her touch with two quick breaks of serve to claim the first set.
Radwanska then switched gears with another quick service break before racing past her German opponent into the second round.
Fourth seed Karolina Pliskova also made an impressive start to the tournament, beating Spain's Carla Suarez Navarro 6-3 6-4.
Suarez Navarro had won three of her five previous meetings against Pliskova but the 25-year-old Czech this time needed just 73 minutes to secure a spot in the next round.
"I think the conditions suit me well, because it's pretty fast -- the balls are flying," Pliskova said on-court after the match. "I think I was serving well, and playing aggressive from the baseline."
"The key was that I wanted to be aggressive, so she doesn't have time to play her game. We played a few times already, always it was kind of tough, but today was the easiest match I've played against her."
One day after sealing a spot in the season-ending WTA Finals in Singapore, fifth seed Caroline Wozniacki advanced into the second round with a 6-1 6-7(4) 6-1 win over home favourite Wang Qiang.
The Dane's next opponent is Anastasia Pavlyuchenkova who raced past American Lauren Davis on Saturday, with a 6-1 6-1 scoreline.
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