Serena Williams battled a misbehaving serve and scorching heat but stayed cool under pressure in a 7-5 6-4 win over Czech Barbora Strycova to reach the Australian Open quarter-finals on Monday. Second seed Williams was broken three times in the opening set at Rod Laver Arena and again when coasting to the finish line in the second but shifted up a gear when it counted to close out the match in one hour and 46 minutes.