The sixth-seeded Dane, made to work hard for her first-round victory over Chinese qualifier Duan Yingying, dropped her first service game on Arthur Ashe Stadium court then never looked back in a 67-minute romp.
"I'm really pleased with the way I was moving today and moving from defence to offense," Wozniacki said on-court after her efficient groundstroke game contrasted with 27 unforced errors from the South African.
Wozniacki, 23, was slowed by a right knee injury last year when she failed to make it out of the first round at the U.S. Open following a first-round exit at Wimbledon.
"I think I always improve as a player. I think I'm playing good tennis. I think I've improved since then," she told reporters.
Neither player registered an ace but Wozniacki's superior return game gave her an upper hand as she put all but three of Scheepers's 47 serves into play.
"She didn't give me any errors in the beginning and I thought I was pressing too much and made some unforced errors," said the South African.
"I was trying to get into the net a little bit and made the mistakes.
"With a player like Caroline, once you get behind, it gets tough to get yourself back in because she's such a tough competitor and doesn't give you anything."
Wozniacki, who reached the semi-finals at Flushing Meadows in 2010 and 2011 and the final in 2009, will next play Italy's Camila Giorgi, a 6-4 7-6 (8) winner over Hsieh Su-Wei of Taiwan.
(Reporting by Larry Fine; Editing by Ian Ransom)
