Medvedev's Rome Open title defence ended by USA's Paul
Second seed Medvedev has never successfully defended an ATP Tour crown and was well below his best, stunned by American Paul who claimed his first win against the former US Open champion.
Paul will play Hubert Hurkacz, who knocked out Rafael Nadal earlier in the tournament, in his first Masters 1000 quarter-final on clay.
"I love it (clay) and that's the first time that I've said that in a long time really," said Paul on court.
"I had a bit of training before the clay court season this year and it really helped. I'm really comfortable and I'm having fun out here."
Medvedev, 28, had a great chance at the Foro Italico after a raft of stars either withdrew or were eliminated early, but instead he became the latest big name to be dumped out of the last major tournament before this month's French Open.
Rome is missing the world's top four ranked men after Novak Djokovic's exit on Sunday and Italian world number two Jannik Sinner and third-ranked Carlos Alcaraz both dropped out injured before the tournament.
Holger Rune, who lost last year's final to Medvedev, and Madrid champion Andrey Rublev -- ranked sixth in the world -- and beaten finalist Felix Auger-Aliassime have also been eliminated.
Hoping to pounce is world number five and 2017 Rome champion Alexander Zverev after sweeping past unseeded Nuno Borges 6-2, 7-5 to set up a quarter-final clash with Taylor Fritz.
Later on centre court, reigning Monte Carlo champion Stefanos Tsitsipas takes on Australia's Alex de Minaur.