The win over world number three Zverev looked unlikely when the 19-year-old dropped the first set and fell behind 2-5 in the second.
But Tsitsipas managed to save two match points and shifted the momentum after edging Zverev in a marathon second-set tiebreak.
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Extending the match paid off for Tsitsipas as Zverev made a number of uncharacteristic errors in a tight third set and he handed the world number 27 victory with a double fault on match point.
The win was the Greek's third straight over a top 10 opponent after he dispatched Dominic Thiem and Novak Djokovic in the previous two rounds.
Next up for Tsitsipas is a showdown with big-serving South African Kevin Anderson, who thrashed Bulgarian Grigor Dimitrov 6-2 6-2 earlier on Friday.
Fourth seed Anderson, runner-up at Wimbledon last month, was never broken and won 81 percent of his first serves.
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