Serena, Djokovic send warning shots to rivals NEW YORK (Reuters) - World number ones Serena Williams and Novak Djokovic ruled supreme on Tuesday, sending ominous warnings to their rivals with dazzling, runaway victories over Spanish opponents at the U.S. Open. Djokovic said he played some of his best tennis on the Arthur Ashe Stadium 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 the National Tennis Center. 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 Li became China's first semi-finalist ever at the U.S. Open by beating Russian Ekaterina Makarova 6-4 6-7 (5) 6-2 on Tuesday at a windy Flushing Meadows. 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. "For me, this is the first time to come to the semi-finals, so I'm very proud of myself," said Li, who looked about to claim victory in two sets after winning the first three points of the tiebreaker but was extended to a third set. 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. "I played really good," acknowledged four-time U.S. Open winner Williams after her 52-minute rout of Suarez Navarro. I'm having a blast this week. For me, I have to stay in that moment of fun, but intensity, but calm. If I can try to do those three things, it works out. It was only the second love-love win in a U.S. 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 Williams, aiming to become the oldest U.S. Open women's winner since tennis turned professional in 1968, has lost just 13 games in her five matches. Djokovic said his game was clicking just as planned. "Today, the second and third set have been some of the best tennis that I've played on Arthur Ashe in my career," said Djokovic, who won the title in 2011 and was a finalist last year and in 2007. "I was wishing to be more aggressive as the tournament progresses," added the Serb, who won the first 25 points on his serve and 28 of 30 points he contested at the net. 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. "In the end, he played the big games when he needed to," said the Australian. Earlier, women's second seed Victoria Azarenka overcame Ana Ivanovic, the 13th seed, 4-6 6-3 6-4 to complete the women's quarter-finals field after their contest was postponed from Monday due to nearly five hours of rain delays. Azarenka, runner-up last year to Serena Williams, will play unseeded Daniela Hantuchova of Slovakia in the last eight. The U.S. Open had been the last grand slam where Chinese women had stalled before reaching the final four. Zheng Jie was the first Chinese player to reach a grand slam semi-final, making the last four at Wimbledon in 2008 and the Australian Open in 2010, but Li has enjoyed even greater success. Two years ago, Li became the first Chinese to make a grand slam final when she finished runner-up in Australia and a few months later she won the French Open to become China's first grand slam champion. Li smashed 44 winners against just 15 for 25-year-old Makarova, though the Chinese struggled with eight double faults. Azarenka and former world number one Ivanovic had even more trouble serving in a match where holding serve was the exception rather than the rule. The 29-game match had 16 service breaks with Azarenka ending it by breaking Ivanovic for the ninth time. It was a big battle. That's what I was expecting from Ana," said Azarenka of Belarus. Ivanovic tried to see the bright side. "It's very encouraging, because I know I'm right there," said the Serb. It's definitely a lot of positives to take from this week and this match. But it still doesn't change. It's disappointing and it hurts. Reporting by Larry Fine; Editing by Mark Lamport-Stokes/Patrick Johnston