Medvedev and Safiullin also combined together for a doubles match, completing a 3-0 clean sweep against the host nation.
Elsewhere, Alexander Zverev sent a warning to the rest of the field at the BNP Paribas Open by easily walking past Frenchman Gael Monfils in their fourth-round clash.
Jelena Ostapenko and Alex de Minaur tuned up for Wimbledonby winning the first grass-court titles of their careers at Eastbourne.
The top seed Russian lost the first set, but came back impressively in the semifinals to defeat Pablo Carreno Busta.
The fourth-seeded Russian was stretched to the limits but survived the contest against qualifier Nikoloz Basilashvili at the Noventi Open semifinals.
The Swiss maestro won the opening set but failed to build on that momentum as he lost the remaining two sets to bow out of the tournament.