Roger Federer (right) exits the court with Andy Murray.

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 Rafa Nadal who rode his luck to beat Bulgarian Grigor Dimitrov.

Federer played sublime tennis to open a two-set lead over Murray but had to withstand a late charge from the Briton before claiming a 6-3 6-4 6-7 6-3 win.

Nadal had dug himself out of a hole to suppress an inspired Dimitrov, winning 3-6 7-6 7-6 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.

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 today, 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 tomorrow’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,” he said.

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 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 in Melbourne last year.

Nadal’s match with Dimitrov turned on the third set tiebreak.

Dimitrov 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 2-1 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, had gone in and he won the third, I was going to keep fighting, because I felt that I was ready for the fight.”

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 the favourite a reminder of how it felt.

The Pole 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.