Clijsters, 28, overpowered the Dane to win 6-3 7-6 (7-4) in scorching temperatures at the Rod Laver Arena. The Belgian, who says she is playing in her last Australian Open, will face Victoria Azarenka in the semi-final.
Earlier on Tuesday, Belarussian third seed Azarenka beat Poland's Agnieszka Radwanska 6-7 (0-7) 6-0 6-2.
Clijsters hit 21-year-old Wozniacki, who has never won a Grand Slam, with a barrage of baseline big-hitting to take the first set 6-3, despite a late rally from the Dane. The second set continued in the same vein with Clijsters racing into a 4-2 lead after breaking Wozniacki's serve for the sixth time. She took the next game, and it looked like victory was close
