The Greek top seed, who reached the Australian Open semi-finals earlier this year, overcame Mikhail Kukushkin of Kazakhstan 7-5 7-6 (5) in just under two hours.
Kukushkin survived an early break point in the match but was broken when serving to stay in the first set at 6-5.
Tsitsipas went 4-2 down in the second set but broke back to level things up at 5-5 and the 20-year-old held his nerve in the tie-break to seal the win.
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