Medvedev, 27, has only once reached the fourth round, though he missed last year's tournament due to the ban on Russian players.
But a rain break at 5-5 in the first set changed the dynamic and Medvedev was generally in control from then on.
"I was pretty nervous, I didn't get to play yesterday so really happy to be back," Medvedev said in a courtside interview.
When they returned 20 minutes later Fery struggled to rediscover his intensity as Medvedev immediately broke and served out the set.
Fery stuck to his guns, charging the net at every opportunity, and though he got a foothold in most Medvedev service games, the Russian was too often able to serve his way out of trouble.
Persons:
Russia's Daniil Medvedev, Britain's Arthur Fery, Toby Melville LONDON, Russian Daniil Medvedev, Arthur Fery, Medvedev, Arthur, I'm, Fery, Roland Garros, ludicrously, Mitch Phillips, Ed Osmond
Organizations:
Lawn Tennis, Croquet Club, Wimbledon, American, Roland, Medvedev, Thomson
Locations:
London, Britain, Russian, British, U.S