The lofty Russian, beaten in the semi-finals last year by eventual champion Carlos Alcaraz, took one hour 46 minutes to dispose of the 88th-ranked New Yorker, who could not cope with his booming serve and whipped forehand.
"I've still never lost on Court One so hopefully I can play a lot more matches on this court," a smiling Medvedev told an appreciative crowd in an on-court interview.
"Last year I said it was unfortunate I had to go to Centre Court for the semis and I lost."
Medvedev, chasing a second Grand Slam title after his 2021 US Open triumph, fired 16 aces on his way to victory over Kovacevic.
"It is never easy to win in straight sets, especially on grass," the former world No.1 said.
But he made it look simple.
He won the first set at a canter after breaking Kovacevic's first service game, took the second with a pair of aces after breaking in the seventh and ran away with the third, clinching it on this third match point with another ace.
He won the first set at a canter after breaking the New Kovacevic's first service game, took the second with a pair of aces after breaking in the seventh and ran away with the third, clinching it on this third match point with another ace.
