Third seed Halep survived a 6-3 4-6 6-4 tussle on a blustery Court Two but struggled to shine against the 170th-ranked qualifier.
The Romanian said she had never seen her next opponent, Swiss teenager Belinda Bencic, in action but since both players have made it as far as the last 32 at Wimbledon for the first time, it will be new territory for both.
"She has nothing to lose against me. Also, I have nothing to lose because is first time in the third round here in Wimbledon. On grass it's always difficult to play," Halep told reporters.
"I will fight for it. I expect a tough match."
Bencic, 17, has form on grass as she lifted the girl's singles trophy at the All England Club last year.
"Tomorrow will be a little bit tough because I heard she's a good player and she's strong," added Halep.
"She's also aggressive. So our games are almost the same."
Since being knocked out of Wimbledon in the second round last year, Halep has raced up the rankings.
She reached the fourth round of the 2013 U.S. Open, the quarter-finals of the Australian Open in January and came within a set of capturing the French Open two weeks ago before losing to Maria Sharapova.
After taking the first set and establishing a healthy lead in the second on Friday, Halep 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 blamed the rejigged schedule for her lapse in concentration.
"I didn't play my best today. I played badly because of the two-day (gap following my last match). It's not easy to wait two days for a match," she said.
(Reporting by Sarah Young; editing by Martyn Herman and Pritha Sarkar)
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