The Russian had an inconsistent run-up to Flushing Meadows but was back to top form on the court where he won his maiden Grand Slam title a year ago, sending across 10 aces and neutralising Kozlov's serve.
"Most pleased to win first of all... not easy conditions," said Medvedev, who repeatedly wrapped an ice towel around his neck to keep cool in the humid, 85-degree Fahrenheit (29.4 Celsius) conditions. "Serve was quite the key today."
The pair traded breaks early in the first set before Medvedev got his motor running, clinching the next four games as Kozlov won fewer than half of his first-serve points.
Kozlov was no match for Medvedev's raw power in the second set. The American scraped his wrist and knee after he dived to retrieve the ball, but ended up falling to the ground heavily in the ninth game that saw Medvedev break him to love.
He called on the trainer to tend to the injuries but Medvedev showed no mercy as he raced through the final set like a bullet train in just 27 minutes to set up a meeting with Frenchman Arthur Rinderknech in the second round.
