Medvedev had needed three sets to oust Italian Lorenzo Sonego a day earlier, but the Russian rode 15 winners, three aces and just six unforced errors to dispatch Spain's Davidovich Fokina in one hour and 17 minutes.
Fifth seed Ugo Humbert of France outlasted third seed Hubert Hurkacz of Poland, 3-6, 7-6, 6-3 to advance to the semi-finals where he will face Medvedev. Humbert saved three match points in the second-set tiebreak. He hit 24 winners in the match lasting two hours and 24 minutes.
Two other seeded players advanced when their unseeded opponents retired due to injury during their quarter-final matches. Second seed Andrey Rublev of Russia eliminated American Sebastian Korda 6-4, 4-3 (retired), and seventh seed Alexander Bublik of Kazakhstan moved past the Czech Republic's Jiri Lehecka 6-4, 4-1 (retired).
Chile Open
Fourth-seeded Alejandro Tabilo won an all-Chilean second-round matchup in Santiago, Chile, beating Tomas Barrios Vera 6-2, 7-5. Tabilo won 91 per cent of his first-serve points and did not face a break point.
Tabilo advances to a quarter-final match against Italy's Luciano Darderi, who downed Argentine qualifier Juan Manuel Cerundolo 6-3, 3-6, 6-3.
Second-seeded Sebastian Baez of Argentina rallied past Peru's Juan Pablo Varillas 4-6, 6-4, 6-2. Baez's quarter-final foe will be eighth-seeded Jaume Munar, who routed Spanish countryman Albert Ramos-Vinolas 6-3, 6-1.
In the other quarter-finals, third-seeded Arthur Fils of France will face Spain's Pedro Martinez, and top-seeded Nicolas Jarry of Chile will go up against French qualifier Corentin Moutet.
Acapulco
Third-seeded Alex de Minaur of Australia overcame a slow start and emerged with a 1-6, 6-3, 6-3 win over fifth-seeded Stefanos Tsitsipas of Greece in the quarter-finals at Acapulco, Mexico.
De Minaur is one win away from his second final of the year, having lost one in Rotterdam two weeks ago. His semi-final opponent will be Great Britain's Jack Draper, who eliminated Serbia's Miomir Kecmanovic 6-2, 6-2.
Second-seeded Holger Rune of Denmark eked out a 7-6, 7-6 victory over Germany's Dominik Koepfer. Rune had a set point at 5-3 in the first set but wound up needing two tiebreakers to advance.
Next up for Rune is sixth-seeded Casper Ruud of Norway, who eliminated Ben Shelton of the United States 6-7, 6-4, 6-4. Ruud squandered two set points in the first-set tiebreaker, but he rallied to take the last two sets by earning one service break in each.
