The third seed eventually won 6-3 4-6 6-4 on a blustery Court Two but struggled to shine against the world No.170.
After taking the first set and establishing a healthy lead in the second she seemed set for routine progress, if a day late after Thursday's rain, but she went off the boil.
Muttering and glancing at her support team, Halep briefly looked as though she might be in trouble but she recovered to forge ahead in a tense deciding set.
She blew two match points at 5-2 but overcame the jitters to claim victory two games later.
Halep has raced up the rankings over the last year, improving with each grand slam since reaching the fourth round of the U.S. Open in 2013. She exited Wimbledon at the second round stage last year.
The Romanian will face Swiss 17-year-old Belinda Bencic, last year's junior champion, next.
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