Alcaraz received a second-set retirement from Dominik Kopefer (ankle) in his opening match, but got the opportunity to stress test his game against the powerful 26-year-old Afrcian on Thursday night.
The youngest US Open top seed in tournament history, Alcaraz defended nine of 10 break points faced and recovered from being a break down midway through the third set.
The Spaniard, who is looking to become the first back-to-back champion at Flushing Meadows since Roger Federer won five straight titles from 2004-2008, improved to 55-6 (18-3 on hard) on the season. He is chasing his seventh title of the season and third career major.
Harris, who frequently challenged Alcaraz with big second serves, was a US Open quarter-finalist in 2021 but missed the last six months of the 2022 season with a wrist injury.
Alcaraz will face a difficult test in the third round against gritty Brit and recent Washington champion Daniel Evans.
On the other hand, Stan Wawrinka rolled back the years on Thursday at the US Open to survive a baseline slugfest against 30th seed Tomas Martin Etcheverry.
Wawrinka, who lifted the trophy at Flushing Meadows in 2016, displayed vintage firepower and pristine fitness as he battled past the Argentine 7-6(6), 6-7(7), 6-3, 6-2 after three hours, 39 minutes.
After a win, Wawrinka set a blockbuster third-round clash against sixth seed Italian Jannik Sinner.
Making his 16th appearance at the season's final major, 38-year-old Wawrinka is the oldest man to reach the US Open third round since a 39-year-old Jimmy Connors was a semifinalist in 1991.
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