Medvedev's win over Team World's Shapovalov earned two points and gave the Europeans a whopping 11-1 overall lead heading into Sunday's final matches at the Boston Garden arena
Russian second seed Medvedev, chasing his first Slam title, eliminated 117th-ranked Dutch qualifier Botic Van de Zandschulp 6-3, 6-0, 4-6, 7-5 at Arthur Ashe Stadium
Medvedev defeated British 24th seed Daniel Evans 6-3, 6-4, 6-3, making his fourth trip to the last eight in the past five Grand Slams as he chases his first Slam title
The world number two Russian needed just 87 minutes, limiting his 2.11m opponent to just eight aces and breaking him three times while saving all four break points he faced
Medvedev lost all his four first-round matches at Roland Garros since his debut in 2017 and has only one win to his name on clay this season.
"I have to say coming here was my first practice yesterday, I was playing amazing so far," Medvedev, who will start his campaign against Kazakhstan's Alexander Bublik, told a news conference on Friday.