court in trouncing Marcel Granollers 6-3 6-0 6-0, and Williams could not have done better, handing Carla Suarez Navarro a 6-0 6-0 beating at Flushing Meadows.
Dominant performances are not out of the ordinary for those rankings leaders but fifth-seeded Li Na provided something special by breaking another barrier for Chinese tennis.
The 31-year-old became China's first semi-finalist ever at the US Open by beating Russian Ekaterina Makarova 6-4 6-7(5) 6-2.
Li pumped both fists in joy after 24th seed Makarova sailed a backhand long to end the two-hour, 20-minute match at Arthur Ashe Stadium as the crowd showered her with cheers.
Other winners were also tested as defending men's champion Andy Murray of Britain worked hard to get past 65th-ranked Denis Istomin of Uzbekistan, 6-7 (5) 6-1 6-4 6-4, and women's second seed Victoria Azarenka overcame Ana Ivanovic 4-6 6-3 6-4 to complete the women's quarter-finals field.
The lone upset by rankings was registered by ninth-seeded Stanislas Wawrinka of Switzerland, who ousted fifth seed Tomas Berdych of the Czech Republic 3-6 6-1 7-6 (6) 6-2
Wawrinka, who has now won five of his last six matches against Berdych, advanced to a quarters clash against Murray.
Li will not have too long to revel in her achievement as the win set up a semi-final date with defending champion Williams.
It was only the second love-love win in a US Open women's quarter-final dating back to 1968, and first since Martina Navratilova subjected Manuela Maleeva of Bulgaria to the embarrassment in 1989. The 31-year-old, aiming to become the oldest US Open women's winner since tennis turned professional in 1968, has lost just 13 games in her five matches.
Djokovic moved into the quarters against Russia's Mikhail Youzhny, who ended the magical run of 2001 U.S. Open winner Lleyton Hewitt by escaping a 1-4 hole in the fourth set and a 2-5 stranglehold in the fifth for a 6-3 3-6 6-7(3) 6-4 7-5 win.
Youzhny, the 21st seed, took pride in outbattling renowned fighter Hewitt in the nearly four-hour match.
"I know he's a great player and he's great fighting player, who is fighting for every point, every match. For me, this way that I beat him today, it's really important," he said.
The 32-year-old unseeded Hewitt, who had upset sixth-seeded former champion Juan Martin del Potro in the second round, gave credit to the Russian.