Li's late-blooming career -- she won at Roland Garros when 29 and at Melbourne Park this year as a 31-year-old -- should also give Nishikori some confidence that his best tennis is ahead of him.
China's Li Na, Asia's first grand slam singles title winner, announced her retirement from tennis on Friday.
The top three seeds have now been sent packing following the first-round exit of Chinese Li Na and the second-round elimination of defending champion and world No.1 Serena Williams.
Li Na lost her first Grand Slam match since winning the title in Melbourne, falling to Kristina Mladenovic of France 7-5, 3-6, 6-1 While Andy Murray beat Andrey Golubev 6-1, 6-4, 3-6, 6-3.
Gone are the days, it seems, when a teenager would jump out of the pack to capture a grand slam.
Serena Williams and Li Na swept past familiar foes at the Sony Open, setting up an exciting showdown for the Miami hardcourt crown.
World number two Li Na powered her way past 11th seed Caroline Wozniacki 7-5 7-5 and into the semi-finals of the Sony Open.
Federer charged into the semi-finals with a straight sets win over Kevin Anderson while Dolgopolov beat Milos Raonic to reach the semis at Indian Wells.
Defending champions Rafael Nadal and Maria Sharapova were upset in the third round of the BNP Paribas Open.
Top seed Rafa Nadal survived a scare from Radek Stepanek before winning his BNP Paribas Open second round match in three tight sets at Indian Wells on Saturday.
Li, who turns 32 next month, lost Australian Open finals to Kim Clijsters in 2011 and Victoria Azarenka last year.
After two weeks of stunning upsets cleared away Li's top competition, she will face No. 20-seeded Dominika Cibulkova.
After two weeks of stunning upsets cleared away Li's top competition, she will face No 20-seeded Dominika Cibulkova, an unheralded but explosive player who has steamrolled through the tournament.
Dominika Cibulkova grabbed control from the first game and overwhelmed fifth seed Agnieszka Radwanska 6-1 6-2 to become the first Slovakian to reach a grand slam final at the Australian Open on Friday.
The 31-year-old, who has reached two of the last three finals at Melbourne Park, blasted the 28th-seeded Italian off the court in 66 minutes
The heat policy was put into effect on Thursday when the temperature topped 42C (108F) in the early afternoon, suspending matches on the outer courts for about four hours.
Safarova, who has never beaten a top-10 opponent in a WTA Tour event, served for the contest in the ninth game of the second set and held a match point in the 12th before Li held, then produced a remarkable tiebreak that she clinched 7-2.