The German world No. 2 defeated Britain's Norrie 7–6(1), 6–4 in one hour and 40 minutes at the Capital Group Diamond.
Zverev was made to work for the opening set, with neither player able to break serve. Norrie earned a set point at 5–6, but Zverev held firm before dominating the tie-break 7–1.
The 29-year-old then produced the decisive break late in the second set, taking Norrie's serve at 5–4 before serving out the match on his first opportunity.
Zverev's serve was a major factor in the victory. He struck 15 aces, made no double faults and won 77% of points behind his first serve. Norrie was unable to create a single break-point conversion opportunity against the German.
The victory continues Zverev's strong run of form following his US Open triumph, Davis Cup success and Laver Cup victory. He now moves into the Beijing last 16, where he will face either China's Juncheng Shang or Argentina's Sebastian Baez.
Zverev is also closing the gap on Jannik Sinner in the battle for the world No. 1 ranking, with the Italian absent from the Beijing tournament.
• Alexander Zverev: defeated Cameron Norrie 7–6(1), 6–4
• Next opponent: Juncheng Shang or Sebastian Baez
• Tournament: China Open, ATP 500
• Venue: Beijing, China
• Round: Last 16