The Swiss superstar built on his fantastic performance against Jo-Wilfried Tsonga to ease his way beyond Murray, who appeared physically tired during the encounter. He'll next meet Rafael Nadal to compete for a spot in the tournament's final.
On this form, belief is rapidly growing that Federer may add to his collection of 17 Grand Slam titles, something that did not look possible after a poor 2013.
Murray began with a bang, claiming the opening point with a rasping backhand return from Federer's serve. Even so, the Wimbledon champion failed to gain any momentum and his opponent took the opening game to 15.
Federer was still finding his range though, and he put too much power on a cross-court forehand, followed by a similar backhand mistake that allowed Murray to level.
As we saw during Federer's mauling of Tsonga in the last round, the four-time Aussie Open winner's backhand appears to be much improved under Stefan Edberg. He exercised this with an excellent shot across court, following on from a simple smash, before capturing the first break with an unforced error from Murray.
The British player looked dangerous when attempting a forehand shot down the line, but Federer's variety meant Murray rarely had the opportunity to settle. Both players held their serve, but Federer never looked like losing the first set.
Federer hit a stunning half-volley followed by an unstoppable backhand winner across court with the score at 5-3. To sum up his dominance, he captured the first set with an ace.
The 32-year-old won 89 percent of his first-service points during the opening set, per the competition's official website, as Murray consistently failed to deal with the first attempt.
Despite winning a 24-stroke rally at the beginning of the second set, Murray's play appeared slightly weak during longer exchanges. Federer regularly approached the net to keep his rival guessing, gaining another break point during Murray's third service game of the second.
A casual forehand miss from the Brit followed an exquisite backhand from Federer, who continued probing with an inventive selection of shots. Two Murray mistakes gifted his opponent the break—an occurrence from which he once again failed to recover.
Even a slip couldn't stop Federer landing a backhand volley at the net. Murray began to inch open minor opportunities—he led 30-15 on Federer's serve with the score at 4-3 to the Swiss—but an inability to push forward with a break left him continually frustrated.
Federer took advantage of his chance to serve out the second set, despite a stunning defensive lob from Murray that crept its way in from the baseline. The struggling Brit followed this with a forehand error, providing Federer with the two-set advantage.
Murray looked to be gaining some sort of rhythm in the third, but Federer's impenetrable defence welcomed anything his opponent had to offer. Although Murray saved a break point at 2-1, Federer got over the disappointment with a love game.
The former champion continued to dominate despite lowering his intensity a little. Federer proceeded to make a huge impression from his serve, always appearing more likely to break.
This happened with the score at 4-4, after a deceiving pickup saw Federer just manage to lob the ball over Murray's reach. With two break points on offer, Murray hit the net.
Amazingly, Murray gained his first break point of the match during the next game, which saw Federer serving for the win. The agitated Brit channelled his frustration to focus on simple returns, forcing Federer into two unforced errors at this vital point in the match.
Both players held serve to send the set toward a tiebreak. Murray jogged to the net to sink a powerful smash, making the score 2-2, but an unforced error gave Federer the lead heading into his serve. Federer's defence was incredible at this point as he stretched his way across court, forcing Murray into another mistake.
Federer was left with two match points to win, the first of which he missed on his serve. Murray fought back in the second, sending a forehand right to the line that Federer could not handle.
Remarkably, Murray landed himself a set point just moments after looking buried. Federer hit another unforced error—his 10th of the set—to keep the match going.
Federer appeared shaken, and he mistimed a couple of shots before holding serve with a neat drop shot in the first game of the fourth set. Murray saved six break points in the next game, which lasted an incredible 20 minutes, before Federer's passing shot plonked out.
At this point, pain was all over Murray's face. His back looked to have stiffened up, and Federer quickly tried to take advantage of that. Murray's backhand lacked its usual power, something his opponent exploited toward a 4-3 lead.
Federer answered an excellent get from Murray with a simple volley at the net in the next game. The Swiss now served for the match for a second time. Though Murray gave everything he had, a simple ace ended his chances of winning the Australian Open for another year.
Federer finished the match with 54 winners, 10 aces and 42 unforced errors. He only managed to win 24 percent of his 17 break points, but won 78 percent of his points from the first serve, per the competition's website.
Murray hit 41 winners, nine aces and 46 unforced errors, securing one of two break chances and winning 67 percent from his first serve.
There's little time for the Swiss star to relax, as his win sets up a huge semifinal tie against Rafael Nadal. The Spaniard overcame Grigor Dimitrov 3-6, 7-6(3), 7-6(7), 6-2 in a quarterfinal fixture that tested the world No. 1's resolve.
It will be interesting to see how Nadal deals with Federer's increasingly aggressive style. The 27-year-old is fitter and stronger than Murray, but if Federer continues to show impressive variety, Nadal's troublesome blister will be tested.
Federer forced Murray into plenty of running. He makes his opponent do the hard work with precision shots, something that is extremely important at the age of 32. Even so, he's looking forward to a brief rest:
With this massive victory confirmed, Federer will tackle Nadal on Jan. 24 for a place in the final.