Roger Federer maintained his outstanding form at the Australian Open to eliminate Andy Murray at the quarter-final stage.

Federer served for a straight-sets win in the third set and held two match points in the tie-break but Murray showed tenacity to take the match into a fourth.

However, in his seventh match after back surgery, he ran out of steam and Federer cruised to an impressive 6-3 6-4 6-7 (6/8) 6-3 victory and a semi-final date with his old rival Rafael Nadal.

This was their 21st meeting and the first time Murray was the higher ranked.

But Federer's form in defeating Jo-Wilfried Tsonga in the fourth round and Murray’s lack of mach practice meant the Swiss maestro started a slight favourite for the contest.

Murray drilled a clean winner off his backhand on the first point but soon Federer was pushing forward and dominating his opponent.

He brought up two break points in the fourth game and took the first when Murray fired a forehand long.

The fourth seed was playing well but Federer was in rare form, barely missing a first serve and timing the ball superbly.

Federer has a new bigger-headed racquet this season and a new man in his corner in Stefan Edberg, and both appear to have renewed his confidence.

Murray appeared confident in his game, too, and was certainly playing at a higher level than he had at any other time in the tournament.

The 26-year-old has consistently shown an ability to step it up against the top players, and this was a real step up after facing three players outside the top 100.

But two forehand errors in a row cost him in the fifth game as Federer broke to lead 3-2.

Murray could not engineer a break point on the Federer serve, and his frustration was evident as the second set slipped away.

The last time Murray had met Federer was in the semi-finals here last year, when he prevailed in five sets for his first win over the Swiss in a grand slam match.

He would have to go five again to repeat that, but that looked a remote possibility as he hung on grimly at the start of the third set.

Federer forced four break points in Murray's opening two service games but squandered all four opportunities.

The Swiss still looked by far the better player, though, and he struck once more in the ninth game when Murray netted a forehand.

The British number one was unhappy that umpire Pascal Maria had allowed a Federer lob to stand even though it looked like the ball had bounced twice.

That left Federer serving for the match but he wobbled, three errors giving Murray his first two break points of the match.

He saved one but on the second a Murray backhand down the line drew the error and he was back to 5-5.

A tie-break would decide it, and it was a real nerve jangler for both men.

Federer looked like he had opened up a decisive lead at 5-2 and he had two match points at 6-4, but Murray played fine attacking points to save both.

The Scot then brought up a first set point and it was Federer who cracked, sending a forehand long.

Murray had built momentum and he opted to take a toilet break at the end of the set, giving Federer more time to reflect on his missed opportunities.

But it was Murray who had the mental letdown and found himself facing three break points in the second game of the fourth set.

He steeled himself to save those and then found himself embroiled in a 19-minute game, which he eventually extricated himself from after fighting off three more break points.

But that effort seemed to take its toll, with Murray dropping the speed on his first serve and beginning to look very weary.

He saved another break point to level at 3-3, but the pressure was growing, and when he slipped 0-40 behind at 3-4, Federer finally broke through.

Another twist seemed possible when the Swiss found himself 0-30 serving for the match for a second time, but he reeled off four points in a row, clinching victory with his 10th ace to move through to an 11th straight semi-final in Melbourne.

 Nadal survived a serious examination by Grigor Dimitrov to progress to the semis.

The Spaniard began the match as the only member of the world's top three in either the men's or women's draw still in the tournament, and for a long time his place looked far from secure.

Nadal did not find anything like his best form throughout the match but Dimitrov's inexperience showed at the crucial moments.

The 22-year-old held three set points in the third set but missed them all and it was Nadal who moved moved through to the last four with a 3-6 7-6 (7/3) 7-6 (9/7) 6-2 victory.

This has been a breakthrough major for Dimitrov, who is beginning to come up with results to match his considerable talent.

He had never previously been beyond the third round at a slam but looked at home on Rod Laver Arena as he broke the Nadal serve at the first opportunity.

The Spaniard had struggled against Kei Nishikori in round four, with a large blister on the palm of his left hand proving particularly troublesome.

Whether that was the reason or not, he certainly could not find his usual feel on the ball.

Dimitrov, who had won sets in all their three previous meetings, capitalised, hitting back from 0-30 down with four straight points to serve out the first set, clinching it with an ace.

It was the first set Nadal had lost all tournament, and the doubts grew when, having broken Dimitrov to start the second set, he handed the advantage straight back with three double faults in one game.

The world number one was rock solid in the tie-break, though, taking it with a superb backhand winner on the run that left him by the umpire's chair.

He stayed in the crouching position, roared and pumped his fists, and when he broke serve to lead 3-2 in the third set, it seemed he had turned the match around.

But a double fault on break point allowed Dimitrov to break back for 4-4, and the Bulgarian will have nightmares about the opportunities he let slip away.

First he held a set point on the Nadal serve after the Spaniard shanked a drive volley, but Dimitrov's attempted return shot vertically off his frame.

His big chance arrived in the tie-break. Very uncharacteristically, at 5-4 and serving, Nadal hooked two forehands wide to hand his opponent a set point.

Dimitrov pushed Nadal out of court with his serve but then missed a forehand he really should have made.

One more set point arrived but Nadal saved that one confidently and then took his first chance when Dimitrov pushed another routine forehand wide.

The Bulgarian had to sit and dwell on what might have been while Nadal had his blister retaped, and it was no real surprise when the top seed moved into a 3-0 lead.

Three match points came and went but on the fourth Dimitrov blazed a forehand wide and Nadal was through to his fourth Australian Open semi-final.