The fourth seeded Indian posted a 6-4 6-2 win over the Estonian in a contest that lasted an hour and 17 minutes at the Olympic Tennis School.
Yuki will next take on Nikola Mektic of Croatia.
The 23-year-old Yuki broke Zopp in the seventh game in the first set to win it comfortably.
In the second set, Bhambri broke his opponent twice in the third and the seventh games to wrap up the match in his favour.
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