The Swiss 2014 champion, whose recent years have been hampered by injuries, won a see-saw encounter with the Russian 6-2 2-6 4-6 7-6 (7-2) 6-2.

Wawrinka, the 15th seed, next plays either compatriot Andrey Rublev or German seventh seed Alexander Zverev.

Fifth seed Dominic Thiem also advanced with a clinical win over Gael Monfils.

The Austrian did not face a single break point in a 6-2 6-4 6-4 win over the French 10th seed that took him to the last eight for the first time at Melbourne Park.

He will now face the winner of Monday's highly anticipated match between world number one Rafael Nadal and Australia's Nick Kyrgios.

Medvedev's five-set misery continues

Wawrinka got off to a blistering start, taking a quick first set with two breaks of serve and showing much of the style that took him to three Grand Slam titles before injuries derailed his career.

But the Swiss, who lost to Medvedev in the US Open quarter-finals in September, then found himself a double break down in the second as the Russian reduced the unforced errors that cost him in the first set and began to take charge.

Medvedev had been billed as one of the main contenders to challenge the 'Big Three' of Nadal, Novak Djokovic and Roger Federer after he took the Spaniard to five sets in September's US Open final.

But after being taken to a tie-break in the fourth, his game began to desert him and he began muttering to himself in frustration.

Once the match went into a final set, Medvedev's record was against him with the Russian having never won a fifth set in five previous attempts.

He went a double break down and allowed the Swiss to serve out the match in comfort after three hours 25 minutes on Margaret Court Arena.

"This was another amazing match, another amazing atmosphere, it was really tough to play against Daniil. The level was super high," Wawrinka said.

Ruthless Thiem plays his 'best match'

Dominic Thiem wrapped up victory over Gael Monfils in an efficient one hour 50 minutes

Thiem, who was beaten by Nadal in the past two French Open finals, was in ruthless form against Monfils on Rod Laver Arena.

The Austrian controlled the match from early on, breaking in the third game. He then consistently put pressure on the Frenchman's serve, creating 14 break points while giving away very little on his own.

The 26-year-old dropped just four points on his serve in the third set, serving out the victory to love.

His celebrations had been briefly put on hold when he thought he had sealed the win with an ace, only for the replay to show it was out.

But he took it on his second serve when Monfils netted a forehand, summing up an erratic performance by the 33-year-old Frenchman, who made 32 unforced errors and has now lost six out of six meetings with the Austrian.

"I think I played my best match so far of this Australian Open. A very, very good feeling," Thiem said.

"The score looks way easier than the match was. I think I was lucky to make an early break in each set and then was managing to hold my serve well. I'm so happy because I'm for the first time in the quarter-finals here."