The seventh-seeded Russian needed two hours and 14 minutes to ease past French qualifier Hugo Gaston 6-4, 6-2, 6-4 and pronounced himself pleased with his progress since a first-round loss to Martin Damm in Winston-Salem last week.
During that match, Medvedev was heard to wonder whether he should drop tennis and take up pickleball - a possibility he was asked about in his on-court interview.
"Last couple of weeks were not easy, but you know how it is - sometimes you lose matches, sometimes you win," he said. "I'm happy that today I managed to produce a high level of tennis.
"I felt like I did everything I wanted to do well. I finished the match strong. I started the match strong. I'm really glad the way I played."
It was a far cry from last year's US Open, when Medvedev lost his cool in a first-round loss to France's Benjamin Bonzi, erupting in the third set when a photographer's mistaken foray onto the court prompted chair umpire Greg Allensworth to award Bonzi a first serve.
Medvedev complained bitterly, urging the crowd to back him, and after finally falling in five sets, he violently smashed his racquet.
The outburst earned him a $42,500 fine, and Medvedev subsequently split with his coach.
