The 24-year-old Romanian was broken serving for the match at 5-4 but she broke right back, and after falling behind 0-30 in the 11th game swept the last four points in a row to end it.
Halep, who reached the semi-finals at Flushing Meadows last year, edged ahead in her rivalry with Suarez Navarro, now leading their head-to-head series 6-5.
"I'm really happy I could win this match. It's really tough to beat her. I just gave everything I had," Halep said in an on-court interview.
The in-form Halep, a three-times winner this year who owns a 23-3 record dating back to start of French Open, will play either top-seeded Serena Williams or unseeded Yaroslava Shvedova of Kazakhstan in the quarters.
The Romanian is bracing for a probable showdown with world number one Williams.
"The next round will be a very tough one, so I want to enjoy this victory today," said Halep.
(Editing by Frank Pingue)
