The top-seeded Dane had to win two tiebreaks to defeat Zahlavova Strycova of the Czech Republic 7-6 (6), 7-6 (9) in a stadium court match that lasted more than 2½ hours. It looked nothing like the 56-minute cakewalk Wozniacki enjoyed in Wednesday's opening match.
"I knew that it wasn't going to be easy. I've seen her before and played her last year here," Wozniacki said.
It sure looked that way at first. Wozniacki led 4-1 in the opening set and appeared ready to quickly oust Zahlavova Strycova.
That's when a frustrated Zahlavova Strycova talked to her coach and promised to play more aggressively. The move worked. She extended points and forced Wozniacki deep into corners to chase down shots.
Zahlavova Strycova held serve twice to force the tiebreak. The 25-year-old fought back in that one, too. After trailing 5-1, she won five straight points to hold a set point of her own. But Zahlavova Strycova sent that chance long and netted the next two points to give Wozniacki the set.
Zahlavova Strycova took a 2-0 lead into the second set. This time, it was Wozniacki's turn to rally. She twice held serve with Zahlavova Strycova ahead to force a second tiebreak for the thrilled fans at stadium court of the Family Circle Tennis Center.
Wozniacki moved in front 5-2, but Zahlavova Strycova fought off four match points. Zahlovova Strycova had a chance to take the set leading 9-8 but sent the ball wide.
Moments later, she put up a defensive lob on a hard-hit ball into the deep right corner and Wozniacki pounded it up into the grandstand.
Zahlavova Strycova said was proud of her performance.
"Against these players, you have to risk a lot and you have to be aggressive," she said.
Wozniacki will play the sixth seed, Yanina Wickmayer of Belgium, for a spot in the semifinals.
Wozniacki reached the finals two year ago before losing to Sabine Lisicki. She retired with an ankle injury in the semifinals last year.
"Every time I go into a tournament, I'm trying to win it," she said. "That's my focus."
Wozniacki said she's counting on more difficult matches ahead in the clay-court season.
"This is the first tournament on clay," she said. "You need to get used to the conditions, you need to get used to sliding. There will be longer rallies in clay, there's no doubt about it, and the matches will most likely be longer."
Stosur arrived here March 29 to practice to defend her crown.
"Anytime you lose early in a tournament, it's not a good feeling," she said. "But especially in a tournament like this where I really enjoyed playing."
McHale, the last American in the singles draw, defeated Daniela Hantuchova 7-6 (3), 6-1.