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The French showman left it late but gave the Ahoy Arena crowd a thrill as he broke in the penultimate game of the third set and served out the win a game later.
Victory sent the 32-year-old into the final here for the second time after reaching the title match in his last Rotterdam appearance in 2016, when he lost to Martin Klizan.
Monfils will take on either top seed Kei Nishikori or former champion Stan Wawrinka in Sunday's final.
Victory was quick revenge for Monfils, who lost to Medvedev a week ago in the Sofia semi-finals, an event which the Russian won.
Medvedev's defeat was only his third loss of the season, leaving his record at 14-3.
The contest featured several momentum shifts and a total of nine breaks of serve in just over two hours.
The 33rd-ranked Monfils at times looked exhausted after points, leaning on his racquet but quickly rediscovering his legs seconds later.
The Frenchman went up an early break in the final set but was hauled back by Medvedev, the fifth seed.
A flicked winner off the Monfils racquet in the ninth game brought up two break points, with the French player earning a 5-4 margin.
A Medvedev backhand into the net a game later handed Monfils the win.
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