
The top-seeded Russian downed his 41st-ranked Belarusian rival 7-6 (10/8), 6-4 in one hour and 51 minutes at the Wimbledon warm-up event.
Medvedev will reclaim the world No 1 ranking from Novak Djokovic on Monday for the first time since March.
Medvedev and Ivaskha, as well as a host of other Russian and Belarusian players, have been banned from Wimbledon following the invasion of Ukraine.
“I don’t have many points to defend on grass and I have some to win, so hopefully I can play well, starting here,” said Medvedev.
“Every round is points and the higher you get, the more you need to step up.”
In Saturday’s semifinal, Medvedev will take on France’s Adrian Mannarino who won the most recent edition of the event in the Netherlands in 2019.
Mannarino saw off Brandon Nakashima of the US 6-7 (5/7), 6-1, 6-4 in his quarterfinal.