The world number three triumphed 6-0, 2-6, 6-2 over 2014 and 2015 champion Nishikori and next faces Britain's Cameron Norrie, a fellow left-hander, for a place in the semi-finals.
It was only the second time in 16 appearances in Monte Carlo that Spain's Rafael Nadal had failed to make it to the semi-finals.
Russian Medvedev, who has won nine matches in a row, beats Spanish Nadal, world number two, 3-6, 7-6 (7/4), 6-3 during their ATP semi final match.
Rafael Nadal inflicts humiliating defeat on Novak Djokovic, thrashing the world number one 6-0 6-2 7-5 and equalling Roger Federer with 20 Grand Slam titles.
Novak Djokovic faces claycourt king Rafael Nadal in a dream French Open final on Sunday with more at stake for the world's two top-ranked players than another Grand Slam title.
World number one Novak Djokovic, the 2016 champion at Roland Garros, reached his fifth final in Paris, defeating fifth seed Tsitsipas 6-3, 6-2, 5-7, 4-6, 6-1.
Claycourt master Rafael Nadal was in action for just 95 minutes, winning 6-1, 6-4, 6-0.
Up to 1,000 spectators have been allowed by the Italian government to be present at the final two days of the tournament in Rome.
Djokovic tied Rafael Nadal’s record by earning his 35th title at a Masters 1000 tournament, overcoming a sluggish start to beat Milos Raonic 1-6, 6-3, 6-4 in the Western & Southern Open final and improve to 23-0 this season.
The 38-year-old Swiss national said he needed follow-up arthroscopic surgery after undergoing a similar procedure in February.
The current world number one, Novak Djokovic has 17 Grand Slam titles to his name - two behind Rafael Nadal and three fewer than Roger Federer.
To the delight of fans, happy to discover some hidden facets of their idols, stars from Karim Benzema to the Brazilian legend Ronaldo and even Rafael Nadal, are dropping their habitual discretion to interact live with their millions of followers.
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