MELBOURNE, Australia — For the second time in the tournament, Simona Halep faced match points and knew one mistake would mean an exit from the Australian Open and the likely loss of her No. 1 ranking.

Germany’s Angelique Kerber, right, shakes hands with Russia’s Maria Sharapova after she won their third round match at the Australian Open tennis championships in Melbourne, Australia, Saturday, Jan.

Romania’s Simona Halep celebrates after defeating Kazakhstan’s Yulia Putintseva in their third round singles match at the Australian Open tennis championship in Melbourne, Australia, Saturday, Jan. 25 ...