Lisicki started the brighter of the two as she secured an early break of serve, but throughout a 63-minute set, both players struggled to hold in the stifling heat in New York.
After three breaks of serve apiece, the set progressed to a tie-break, which Lisicki took 8-6 after saving a set point from Halep.
The Romanian called for the trainer and immediately lost her serve after the restart, but in the next game, she struck back to remain competitive in the match.
Halep appeared to recover from the hamstring problems that had been troubling her, breaking the German early in the second as she attempted to level the match.
Lisicki won three games in a row to get the set back on level terms, but struggled to close out her own service game while trailing 6-5, allowing the second seed to take the match to a deciding set.
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It was the German who struggled with fitness midway through the third though, as Lisicki seemed to be suffering from cramps, allowing Halep to get the first break on the board, opening up a 4-2 lead.
Lisicki never shook off the cramp, allowing her opponent to pick up the next two games, securing her spot in the last eight where she will face Victoria Azarenka.