The Russian blazed past Stefan Kozlov and Arthur Rinderknech in the last two rounds and looked every bit the champion again, as he fired 12 aces and converted six of 12 break points to comfortably dispatch his 22-year-old opponent.
"If you ask me what I could improve, I don't see many things," Medvedev said of his title defence. "Maybe a little bit less double-faults, but that's if we're trying to dig somewhere. If not, high-level match.
"If I continue this way, have good opportunities to do something big. But the next match is not easy. Going to try to recover well and be 100% for the next one."
Medvedev's win in front of an emotional Arthur Ashe Stadium crowd following Serena Williams' loss to Ajla Tomljanovic meant he has reached the round of 16 at Flushing Meadows for the fourth straight year.
Wu, who became the first Chinese man in US Open history to reach the third round, was plagued by several unforced errors in the clash as Medvedev prevailed in an hour and 55 minutes.
After sealing a closely contested first set, Medvedev broke early to race ahead 5-1 in the next and closed it out in style to take full control of the contest.
The third set followed a similar pattern as Wu crumbled under the relentless pressure, with Medvedev staying on course to become the first player to win consecutive US Open titles since Roger Federer's run of five between 2004 and 2008.
But a defeat to Kyrgios in the next round would see Medvedev lose his number one ranking to Rafa Nadal after the tournament.
"We've played great matches. All have been quite tight on the scoreboard," said Medvedev, who has lost three of his four previous meetings with Kyrgios, including the last one in Montreal less than a month ago.
"It's 3-1 to him but I'll try to do better this time and it'll be a great match for people to watch."
Medvedev said he was aware of what he needed to do this weekend against the temperamental Australian, who is playing the best tennis of his career, having finished runner-up at Wimbledon and winning in Washington, D.C. in the lead-up to US Open.
"I don't think we are friends. When I say 'friends', we haven't been to the bar together," Medvedev said with a smile.
"I feel like we respect each other a lot. On the court also we never really had any fight or anything, which can change any moment. We are both quite electric. You never know what's going to happen in the future.
"Nick is a little bit different from other tennis players sometimes on the court. That's his choice. That's his life. I'm not the one to judge."
