World number one Medvedev fought back from a set down to defeat Aslan Karatsev 3-6 6-4 6-2 and advance to a quarter-final against fifth seed Roberto Bautista Agut, who was granted a walkover after Nick Kyrgios pulled out with an abdominal issue.
The Russian got just 48 per cent of his first serves in during a blustery opening set before improving to 68 per cent in the second and controlling the decider as Karatsev struggled with injury.
"It was tough to play [in] rhythm. It felt like many points were just whoever managed to put the ball in the court was going to win the point," Medvedev said. "It was not easy but I'm happy to win because that's the most important [thing].
"Last year was amazing. I played great tennis. Hopefully I can do the same this year. I like it here in Mallorca, so hopefully I can stay as long as possible in the tournament."
Alongside Medvedev and Bautista Agut, Stefanos Tsitsipas is the only other seed left in the draw after he overcame Ilya Ivashka 6-4 6-4.
Denis Shapovalov was a 6-4 6-1 loser against Benjamin Bonzi, Pablo Carreno Busta went down 6-3 6-4 to Antoine Bellier and Sebastian Baez's meeting with Daniel Altmaier ended in a 6-2 2-6 6-4 defeat for the Argentine.
At the Eastbourne International, second seed Sinner suffered a 6-3 3-6 6-3 loss to Tommy Paul as he made his return from a knee injury sustained at the French Open.
World number 13 Sinner remains without a grass-court win in his ATP Tour career, while Paul will next face defending champion Alex de Minaur, who overcame Lorenzo Sonego 7-6 (7-3) 6-2 in a repeat of last year's final.
Jack Draper defeated fourth seed Diego Schwartzman 7-5 7-6 (7-3) to advance to the quarter-finals and Cameron Norrie cruised past Brandon Nakashima in straight sets.
There were also wins for Maxime Cressy, Alexander Bublik and Taylor Fritz.