Gasquet underwent groin surgery in January and returned to competition in May.
Sunday's championship final in the Western & Southern Open at the Lindner Family Tennis Center - Medvedev's third final in three weeks - would break the tie and the victor would become the new Cincinnati Masters titlist.
The complexion of the match changed in a heartbeat as Medvedev overpowered the previously dominant Djokovic.
Medvedev has arguably been the best player on the ATP Tour over the past three weeks.
Medvedev explained why he had switched tactics.
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"I don't know how I turned it around, I was so exhausted after the first set and I thought I might not be able to keep up the intensity", said Medvedev, who has competed in 15 hardcourt matches since July 30.
"Novak had been destroying me on second serve, so I just went for it", Medvedev said.
Medvedev added it was par for the course to go for broke on his second serve when trailing in a match. At one moment, I said to myself why do a normal second serve if I'm going to lose the point.
At three games all in the second set and 0-30 down on serve, Medvedev begin powering down second serves to reel off four successive points, including a second-serve ace, before breaking Djokovic in the next game with a down-the-line victor.
Medvedev, who also beat Djokovic at Monte Carlo in April, will play Belgium's David Goffin in the final on Sunday, with the victor set to claim their first-ever Masters title.
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Keys, the 2017 US Open runner-up, defeated compatriot Sofia Kenin 7-5, 6-4.
"He played incredible tennis from 4-3 in the second set". The crowd gave me so much energy. "He's working his way to top 5".
World No 8 Medvedev beat the tournament's favourite Djokovic 3-6, 6-3, 6-3 in one hour and 43 minutes.
"I thought I played a really good match", Djokovic said after his 3-6, 6-3, 6-3 loss. "My mentality was the best, my serve was the best, my tennis has been really consistent".
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It's worth noting, though, that Goffin hasn't needed to get past a top 20 player in order to get to the final - he's definitely benefited from the draw opening up for him, and with this in mind, it's actually quite hard to assess his level this week.