The world number two from Belarus next faces Czech player Nikola Bartunkova in the round of 32.
Sabalenka groaned over a smattering of unforced errors during the 62-minute match but had the clear edge over Mexico's Zarazua, ranked 94th, breaking to win on the second time of asking.
"I was just trying to stay focused on myself. Tried to stay aggressive on my serve, on the return as well," the 28-year-old said.
"So happy with the game I played today."
Next on centre court, Novak Djokovic was scheduled to play Chinese world no. 104 Bu Yunchaokete in the second round of the men's 500-level event also taking place.
The 39-year-old Serbian great owns six titles from the China Open and is looking to extend an extraordinary unbeaten streak in Beijing.
Osaka and Andreeva through
Earlier on Friday, Japan's Naomi Osaka wrestled back control to survive her second-round clash with Uzbekistan's Maria Timofeeva 6-3, 3-6, 6-3.
The four-time Grand Slam champion next plays Sara Bejlek of the Czech Republic.
French Open champion Mirra Andreeva of Russia overcame a first-set wobble to beat Chinese wildcard Yuan Yue 3-6, 6-0, 6-0.
Wimbledon winner Linda Noskova, a 2025 Beijing finalist, beat Elena-Gabriela Ruse 6-4, 6-1.
Andreeva next faces Uzbekistan's Polina Kudermetova, and Noskova will meet Switzerland's Viktorija Golubic in the third round.
In the men's draw, a series of searing forehands from Daniil Medvedev sent qualifier Pablo Carreno Busta home 6-4, 6-2, earning the Russian world number six a second-round meeting with Germany's Jan-Lennard Struff.