World No 2 Medvedev moves on to the round of 16 where he will face Bulgaria's Grigor Dimitrov, who cruised past American Reilly Opelka.
Medvedev didn't face a break point, and converted three of his seven break chances against the American to wrap things up in 72 minutes.
Beating the eighth-seeded Andreescu made Rogers 24-19 in 2021, giving her a career high for wins in a season.
The 18-year-old became the first player to emerge from qualifying to win a Grand Slam tournament when she beat another teenager, 19-year-old Canadian Leylah Fernandez, 6-4, 6-3 on Saturday.
Americans Shelby Rogers, Jenson Brooksby and Reilly Opelka won on Day 6 of US Open with Novak Djokovic taking another step towards calendar Slam.
Reigning Wimbledon champion Barty won 11 of 14 games after dropping the first set, only for Rogers to capture five of the last six games for a shocking 6-2, 1-6, 7-6 (7/5) triumph.
Day 2 of US Open had its fair share of drama for some while it was smooth sailing for the big guns Novak Djokovic, Ashleigh Barty, Alexander Zverev - to name a few.
US Open 2021: Novak Djokovic launches calendar Slam quest with win; qualifier stuns Pablo Carreno Busta
Fourth-seeded Zverev, coming off Japan gold and a title two weeks ago at Cincinnati, dispatched American Sam Querrey 6-4, 7-5, 6-2 in a first-round match at Arthur Ashe Stadium.
Jabeur won her 36th match of the season, second-best on the Tour behind Sabalenka, with 37.
Andreescu, the 2019 US Open champion, who missed the entire 2020 season with injury, has played little in 2021 and hadn't won a match since reaching the second round at Eastbourne in June.
Tokyo Olympics 2020: Empty stadiums, pandemic, scheduling get in the way of tennis players and Olympic dream
A big bunch of tennis players are giving the Tokyo Olympics a miss due to injuries, scheduling concerns, pandemic, absence of fans and strict COVID-19 rules.
Goffin joins several high-profile players who have already withdrawn from the Olympics.
Andreescu joins several high-profile players who have already withdrawn from the Olympics.
Wimbledon 2021: Fighting Murray, flawless Djokovic slip into third round; Sofia Kenin loses to Madison Brengle
World number one Djokovic, chasing a sixth Wimbledon and record-equalling 20th Grand Slam title, won 6-3, 6-3, 6-3 over the 102nd-ranked South African.
Wimbledon 2021 women's singles preview: Serena Williams sets sights on number 24, Angelique Kerber hits form
Ahead of Wimbledon, we take a look at the women's singles draw and (bravely/foolishly) attempts to determine the potential outcome of all four quarters.
Eastbourne defending champion Karolina Pliskova beaten by Camila Giorgi, Jelena Ostapenko, Elina Svitolina win
The fifth-seeded Czech was beaten 2-6, 6-2, 6-2 by Italian qualifier Giorgi in the first round of the Wimbledon warm-up event on England's south-coast.
Swiatek, who turns 20 next week, was the lowest-ranked woman, then 54th in the world, to win the French Open, shifted from its traditional May-June slot last year due to the Covid-19 pandemic.
The Canadian, who is the top seed in the tournament, felt a twinge during her 6-1, 6-4 win against Maryna Zanevska of Belgium on Tuesday.
The 19-year-old, who will head to Roland Garros in a fortnight as defending French Open champion, beat Karolina Pliskova 6-0, 6-0 in the final in Rome at the weekend to climb six places to ninth, leapfrogging her Czech opponent who slips to tenth.
Andreescu had hoped to be ready for the WTA tour's clay-court swing leading up to the French Open, and had received a first-round bye in Rome.