* Chinese Li wins last four games to seal victory
* Azarenka fights back to beat Ivanovic
* Djokovic dazzles to sweep past Granollers (Adds quotes, Djokovic win)
By Larry Fine
NEW YORK, Sept 3 (Reuters) - Li Na broke another barrier for Chinese tennis, becoming China's first semi-finalist at the U.S. Open by beating Russian Ekaterina Makarova 6-4 6-7(5) 6-2 on Tuesday at windy Flushing Meadows.
The 31-year-old, fifth-seeded 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 and holding a 4-2 lead.
"After I lose the second set, I was sad. But I just told myself to go point by point."
Li's win over the Russian left-hander helped restore order after Monday's shocking straight sets, fourth-round surrender by Roger Federer to Tommy Robredo.
Men's top seed Novak Djokovic was dazzling in a 6-3 6-0 6-0 demolition of unseeded Marcel Granollers of Spain to reach the quarters against 21st-seeded Russian Mikhail Youzhny, who ended the run of 2001 winner Lleyton Hewitt 6-3 3-6 6-7 (3) 6-4 7-5.
"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, which is saying something given his charge to the title in 2011 and runs to the final in 2007 and 2012.
"I was wishing to be more aggressive as the tournament progresses and to be able to stay committed to play every point, to win every point, regardless of what's the score," said the Serb, who won the first 25 points on his serve.
"So I'm very happy with my mental state, how I feel physically, and the way I played. It's definitely coming at the best possible time."
Youzhny, the 21st seed, outbattled renowned fighter Hewitt by overcoming deficits of 1-4 in the fourth set, and 2-5 in the fifth, as he won the last five games of the match.
"Obviously, it could have gone either way," said 32-year-old unseeded Hewitt, who had upset sixth-seeded former champion Juan Martin del Potro in the second round and was trying to reach the U.S. Open quarter-finals for the first time in seven years.
"There were a lot of momentum changes. In the end, he played the big games when he needed to."
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.
The world number two Belarussian, U.S. Open 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 2011 French Open to become China's first grand slam champion.
Li's semi-final opponent will be either world number one Serena Williams or Spain's Carla Suarez Navarro, who were meeting in Tuesday's feature night match.
"I will lie down in the bed, take some chips and watch the match," Li said about scouting her next opponent. "They will just fight and I'll relax."
Li took the fight to Makarova in her quarter-final, smashing 44 winners against just 15 for the more defensive 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 the day's opening match, where holding serve was the exception rather than the rule.
In a match of 29 games, there were 16 service breaks with Azarenka fittingly ending the two-hour, 10-minute struggle by breaking Ivanovic for the ninth time of the contest, when Ivanovic netted a backhand on the fourth match point.
Azarenka had her serve broken seven times and committed nine double faults, while Ivanovic lost nine of her service games and made eight doubles after playing a brilliant first set.
"It was a big battle. That's what I was expecting from Ana," said Azarenka.
Ivanovic, making a concerted effort to climb back up the rankings after a long slump, tried to see the bright side.
"It's very encouraging, because I know I'm right there," she said. "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)