Roger Federer produced one of the most memorable wins of his distinguished career on Tuesday, somehow finding a way past Tennys Sandgren and progressing into the semi-finals of the 2020 Australian Open, 6-3, 2-6, 2-6, 7-6 (8), 6-3. 

Sandgren rallied after falling behind in the first set; he had seven match points in the fourth, with Federer struggling with an injury issue.

However, the 20-time Grand Slam champion managed to dig deep to save them all and claw his way back to parity in the match.

In the decider, Sandgren was stunned, and when Federer broke, there was no coming back for the American.

Here is the moment Federer progressed, setting up a last-four showdown with either Novak Djokovic or Milos Raonic:

Afterwards, the third seed said he thought he was fortunate to get through the contest: 

The opening set saw Federer on form, and while Sandgren was determined and diligent, the class of the Swiss was too much for him to cope with. A 6-3 stanza looked poised to be a precedent for a quick day's work for the great man.

However, in the second some raggedness crept into Federer's play, with Sandgren's serve starting to click into gear. 

In the third set, there was no significant response from Federer, with Sandgren beginning to dictate the points and get stuck into his opponent's serve. 

After a two breaks in quick succession for the American in the third, Federer seemed to be struggling with an injury issue and took a medical timeout; Jose Morgado of Record noted his serve speeds were down: 

As Ben Rothenberg of the New York Times noted, the usually cool Federer was beginning to look uncharacteristically flustered out on court, as Sandgren edged in front:

In the fourth set, the underdog had his opponent on the brink three times at 5-4, although he planted three match points into the net to allow Federer off the hook.

With Federer clearly struggling to move with his usual grace, he somehow forced a tiebreak but when 6-3 down in it his hopes of making the semi-finals appeared to be over. Yet the 38-year-old somehow clung on, with a combination of brilliant play and Sandgren's nerves keeping the match alive, with three more match points passing him by.

A rasping serve from Sandgren gave him his seventh match point of the match, but once again he was tentative in the following exchanges, allowing Federer off the hook. The Swiss then forced a mini-break and his first set point, which he seized.

Christopher Clarey of the New York Times summed up an incredible spell of tennis:

Per The Tennis Podcast, both men were struggling to grasp their opportunities when they surfaced: 

At the end of the fourth set, Federer was able to find some fluency in his movement again, which transferred into the fifth against a noticeably dejected Sandgren.

In the early stages of the decider, the American was clinging on to his serve, with Federer suddenly finding a way of getting into the points again when returning. After fashioning a 3-2 lead, the Swiss broke, consolidated and there was ultimately no way back his opponent.