The 22-year-old progressed 7-6 (7/4) 6-3 against the world number 42 in China.
Unseeded Boulter will play Barbora Krejcikova in the last 16 after the Czech qualifier progressed due to the retirement of Ukraine’s Kateryna Kozlova in their first-round meeting.
With her match against Sakkari on serve, Boulter had the first opportunity of a breakthrough but failed to capitalise on four break points during the seventh game of a tight opening set.
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Four successive breaks of serve, two for each player, led to a tense tie-break and Boulter held her nerve to put herself in control.
The world number 101 backed it up by breaking the Greek during her opening service game of the second set and then squandered a break point to go 4-0 up.
Sakkari twice moved to within two games of her opponent but Boulter served confidently and made the most of her second match point.
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