Zverev, who came into the match with a 6-9 record versus Medvedev and having lost all three of their meetings this year, broke the Russian three times and saved six of eight break points to seal victory in two hours 32 minutes.
"Very difficult conditions but also a very difficult opponent," German 16th seed Zverev said in his on-court interview. "He is somebody that gives you absolutely nothing. You have to win the match yourself and that's what I did today and I am pleased with that."
Medvedev double-faulted to hand an early 4-3 lead to Zverev and had a glorious chance to get the match back on serve in the next game when he led 40-0 but came up short as the German 16th seed held before taking the opening set.
Medvedev moved ahead in the second when Zverev pulled a forehand wide to hand over a break and 4-2 lead but the German broke back immediately before the world number three dealt a crushing blow with a break to love to force a decider.
There was little to separate the players in the third set, which was deadlocked at 4-4 when Zverev set up a break point opportunity with a supreme dipping crosscourt forehand winner that Medvedev followed up with a double fault.
Zverev seized his opportunity and sealed the high-quality encounter on his first match point when Medvedev sent a service return long.
