* Nadal fights back from a set down
* Federer beats Murray
* Radwanska upsets Azarenka
* Cibulkova hammers Halep
By Nick Mulvenney
MELBOURNE, Jan 22 (Reuters) - Roger Federer's revival gathered pace as he edged Andy Murray in a late-night dog fight to set up a blockbuster Australian Open semi-final with world No.1 Rafa Nadal who earlier on Wednesday had rode his luck to beat Bulgarian Grigor Dimitrov.
Swiss Federer played sublime tennis to open a two-set lead over Murray but had to withstand a late charge from Briton before claiming a 6-3 6-4 6-7(6) 6-3 win in the first "Big Four" clash of the year.
Nadal had dug himself out of a hole to suppress an inspired Dimitrov, winning 3-6 7-6(3) 7-6(7) 6-2 after his opponent had squandered a golden chance to win the third set.
Victoria Azarenka could only blame herself after she was earlier shown the door 6-1 5-7 6-0 by Agnieszka Radwanska to leave the tournament without a defending champion in the last four of either draw for the first time in the professional era.
After ending Azarenka's hopes of a third straight title, Radwanska will face Slovakia's Dominika Cibulkova, who crushed Simona Halep 6-3 6-0, to decide who meets China's Li Na or Canadian teenager Genie Bouchard in the final.
With Tomas Berdych meeting Novak Djokovic's conquerer Stan Wawrinka in the first men's semi-final on Thursday, the winner of the Nadal-Federer clash will like their chances of adding another grand slam title to their considerable hauls.
"It's going to be a good match," 32-year-old Federer, who had reached only one grand slam semi-final since claiming a 17th major title by beating Murray in the 2012 Wimbledon final, told reporters of Friday's next installment of his Nadal rivalry.
"It's going to be brutal and all those things. Looking forward to slugging it out with him in a couple of days."
A free-flowing Federer had looked in total command against Murray until late in the third set when he served for the match at 5-4, having just broken the fourth seed's serve.
Murray broke back and forced a tiebreak and then hung in doggedly to overturn a 4-6 deficit and force a fourth set.
Federer shrugged off missing his chance, however, keeping his cool through an hour-long fourth set to outlast a tiring Murray and avenge his defeat in the semi-finals here last year.
"I've been in these positions before," Federer, who has reached the semi-final for an 11th straight year at Melbourne Park, said. "For me it was just a matter of staying calm and forgetting about it a little bit.
"The match was great until that point when I couldn't get it done really."
Having lost three finals, Murray has endured plenty of heartache in Melbourne but the Wimbledon champion was philosophical in defeat given his recent return to action after back surgery curtailed his 2013.
"I've come a long way in four months," he said. "Obviously right now I'm very disappointed.
"Wasn't too far away in the end."
Thirteen-times grand slam champion Nadal's match with Dimitrov turned on the third set tiebreak and there was enough entertainment in those 16 points alone to justify the ticket prices.
Dimitrov, desperate to shed the "Baby-Fed" tag he acquired because of his stylish game and step out of the shadow of girlfriend Maria Sharapova, had produced some brilliant tennis in his first grand slam quarter-final to take the first set.
Struggling to maintain his control over his racket at times because of a painful blister, Nadal almost inevitably battled back to even up the match but Dimitrov was not finished.
The 22-year-old had three chances to go two sets to one up but shanked a return to blow one at 6-5 on Nadal's serve, blew another in the tiebreak when he went long with a forehand and a third when the Spaniard cut off a volley.
"I got lucky," said Nadal. "(But) if that ball, that forehand from him, goes in and he win the third, I going to keep fighting, because I felt that I was ready for the fight.
"I will keep fighting until the end."
Nadal made the most of the reprieve to clinch the tiebreak 9-7 and race away with the fourth set, leaving Dimitrov shattered.
"I shed a few tears, but it should hurt. It should hurt. And it does hurt," he said.
Radwanska went for broke to snap Azarenka's 18-match winning streak at Melbourne Park with a thoroughly deserved victory.
Azarenka came into the match as the only woman not to have given up a set in the tournament but Radwanska, who had lost 12 of their 15 previous meetings, wasted no time in giving her a reminder of how it felt.
The Pole, scuttling around the court to retrieve everything thrown at her, raced out to a 5-0 lead and went a set up after 33 minutes.
Azarenka charged back to clinch a tight second set with a fierce forehand winner but the shriek with which she celebrated failed to galvanise her and Radwanska whipped through the decider in another half an hour.
"I really had nothing to lose," said Radwanska, the losing finallist at Wimbledon in 2012.
"She was defending the title, not me. I was really trying to play my best tennis, go for every shot I could."
Azarenka made 47 unforced errors and knew she made a hefty contribution to her own downfall but leavened her self-flagellation with some praise for the fifth seed.
"It's not the end of the world," she said. "I'm not happy with what I did today (but) I can't take away what she's done. She played amazing."
An aggressive gameplan also paid dividends for 20th seed Cibulkova as she demolished a hapless Halep to reach her maiden grand slam semi-final. (Editing by Peter Rutherford and Martyn Herman)