Neither player was particularly convincing in the early stages, with each of the first four games going against serve, but it was Krejcikova who settled quicker to take the first set 6-3.
She then brought the second set back to 5-5 after being 5-2 down, but Halep managed to see it out to level the match, before going on to seal the 3-6 7-5 6-2 win in the decider.
Top-seed Halep will face Poland's Magdalena Frech – ranked 174 in the world – in the quarter-finals after she saw off Arantxa Rus 6-3 2-6 6-4.
The day began with what turned out to be a gruelling encounter between Eugenie Bouchard and Tamara Zidansek, but the Canadian – who is attempting to climb back up the rankings after slipping to 330 – prevailed to reach her second WTA quarter-final of the year, winning 7-6 (7-2) 6-7 (2-7) 6-2 in two hours, 56 minutes.
Sara Sorribes Tormo had no such difficulty against Laura Siegemund as she emerged 6-2 6-3 victor, but she will have to wait until Friday to find out her next opponent after Irina-Camelia's meeting with Leonie Kung was suspended due to poor light.
Kung had just won the first set 7-6 (7-3).