Pegula needed just 56 minutes to trounce Sofia Kenin, the former Australian Open champion now ranked 110th, 6-3, 6-1.
Seventh-seeded Medvedev downed US wild card Sebastian Gorzny 6-1, 6-3, 7-5.
Pegula, who is among a trio of players who could supplant Aryna Sabalenka atop the world rankings in New York, dropped just seven points on serve.
"I was just trying to stay focused on what I needed to do," said the 2024 US Open runner-up, who next meets another former finalist, Leylah Fernandez.
The Canadian breezed past Thailand's Mananchaya Sawangkaew 6-4, 6-1.
Medvedev, who has struggled in the hard court build-up to the year's final Grand Slam, dominated 731st-ranked Gorzny.
He fired 14 aces and saved the lone break point he faced, although he was distracted briefly when a pair of small birds perched on the Louis Armstrong Stadium net and he was forced to replay a point he thought he'd won.
"I saw them straight away and I thought the point would stop straight away and we didn't," Medvedev said. "And the moment I hit the winner we stop. I was not happy with the decision."
He was happy enough with his game, however.
"The first two sets he was not playing the best tennis of his life maybe. The third set was much more competitive," Medvedev said.
"At the same time I feel like I had more break points and put more pressure on him."
Brandon Nakashima, the in-form 16th seed who was also reckoned to be among the contenders to end American men's 23-year major title drought, was upset by 46th-ranked compatriot Alex Michelsen 6-3, 6-4, 6-4.
Spain's Paula Badosa, who was serving for her match when rain stopped play on Tuesday night, returned to finish off Australian Daria Kasatkina 6-1, 6-4 and book a second-round clash with fourth-seeded American Coco Gauff.