Kyle Edmund’s first-round defeat to Jeremy Chardy opened the door for Norrie, but he needed a deep run in China to take the British No 1 spot.
It means Dan Evans is set to become the highest-ranked Briton after the returning Andy Murray - who needed to win the title in Shanghai to reclaim it himself - lost to Fabio Fognini.
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Norrie lost 6-3 6-1 to Medvedev, who is through to face Vasek Pospisil in the next round.
Edmund slips out of the ATP top 50 following his sixth defeat in a row, while for Evans the British No 1 status would mark an incredible change in fortunes for the 29-year-old.
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Back in 2017, Evans received a one-year ban from the International Tennis Federation for testing positive for cocaine.
He returned from the doping ban in mid-2018, and has risen up the rankings from 1195th in May 2018 to 43rd as of Monday.
Evans and Norrie played together at the US Open, losing to top seeds Juan Sebastián Cabal and Robert Farah in the second round.
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