The victory extended Alcaraz's match-winning streak at the Grand Slams to 17 following his triumph at Flushing Meadows last year and his Australian Open win in February, the latter helping him to become the youngest man to complete the career Grand Slam.
The Spaniard arrived in New York having missed nearly five months of action with a wrist injury and has looked increasingly assured with each passing round, although Wu briefly halted his early momentum by recovering a break in the opening set.
World number 113 Wu, bidding to become the first Chinese man to make the last 16 of a Grand Slam in the professional era, was unable to build on that bright spell on Arthur Ashe Stadium and Alcaraz reasserted his authority to move ahead.
The seven-times major champion's speed around the court and relentless accuracy were on full display in the second set, but Wu's stubborn resistance drew a scream of frustration from him before he conjured up the magic needed to double his lead.
With the finish line in sight, the 23-year-old unleashed a huge roar as he broke for a 3-1 lead in the third set and pulled clear of Wu for a comprehensive victory that set up a meeting with American 20th seed Tommy Paul.
Meanwhile, Daniil Medvedev has continued his strong form at the US Open, beating Arthur Rinderknech 6-4 6-4 6-4 to reach the fourth round as he looks to make a deep run in New York.
The seventh-seeded Russian arrived at Flushing Meadows with plenty of room to move up the rankings, defending only 10 points after a chaotic first-round exit a year ago.
He also has history on his side, having won the US Open in 2021.
The only real scare for Medvedev came early, when he dropped serve for the first time in the tournament and Rinderknech, the world number 29, moved 4-2 ahead.
The 30-year-old Russian recovered quickly, winning four straight games to turn around the set and take the lead.
From there, Medvedev tightened his grip.
He did not face a single break point in the second set, serving with authority while converting his only break opportunity to move two sets ahead.
He carried that momentum into the third, breaking Frenchman Rinderknech in the opening game to take a decisive lead and close out his 35th win of the year.
The victory avenged Medvedev's most recent meeting with Rinderknech, who beat him at the Shanghai Masters, while the Russian had won their previous encounter, also at the US Open, in straight sets in the 2022 second round.
Medvedev will face either Frances Tiafoe or Rinderknech's cousin, Monaco's Valentin Vacherot, in the fourth round, where he will bid to reach the last 16 in the tournament for the seventh time in the last eight seasons.
