Roger Federer was not going to go gently, of course, no matter how daunting the number of match points — his opponent accumulated seven! — no matter how achy his 38-year-old legs, no matter how slow his serves, no matter how off-target his groundstrokes.

Federer still plays for the love of these stages and circumstances. Down to his very last gasp, time and again, against someone a decade younger, 100th-ranked Tennys Sandgren of the United States, Federer somehow pulled off a memorable comeback to reach the Australian Open semi-final for the 15th time.

Despite all sorts of signs he was not quite himself for much of the match, Federer beat the biceps-bearing, hard-hitting, court-covering Sandgren 6-3, 2-6, 2-6, 7-6 (10-8), 6-3 on Tuesday in a rollicking quarter final that appeared to be over long before it truly was at the Rod Laver Arena.

“I’ve played a lot of tennis throughout my life and sometimes you feel a little bit funny and I started to feel my groin and my leg tighten up and I really struggled in defence. I don’t like to call the trainer ever because it’s a sign of weakness or whatever. The best thing about the groin injury is that you go off the court and nobody knows what it is. At the end I was like whatever, I’m going to have some extra treatment on my leg. People probably know I’m not 100 per cent,” 20-time Grand Slam champion Federer said after wrapping up the match in three hours and thirty-one minutes.

“I just said I believe in miracles, there could be rain, there could be other stuff. (The injury) wasn’t bad enough where I thought it was going to get worse. It was just stiff and tight. (I thought) just let him finish me off in style and he didn’t do that so I’m incredibly lucky today.

“...I don’t deserve this one, but I’m standing here and I’m obviously very, very happy,” he said.

Federer was involved in a dispute with the chair umpire over cursing; he left the court for a medical timeout early in the third set, then was visited by a trainer later for a right leg massage. And, above all, found himself in a tense tussle with Sandgren, a 28-year-old from Tennessee.

After rolling through the second and third sets as Federer’s serves dropped from an average of 180kmph to 169kmph and his unforced errors totalled 30, Sandgren led 5-4 in the fourth set.

With Federer serving, Sandgren had a trio of opportunities to complete a career-defining victory. On the first, Sandgren dumped a backhand into the net. On the second, he pushed a forehand wide. On the third, another forehand found the net. On they went to a tiebreaker, which included the bizarre sight of a ball-kid running into Sandgren’s right calf at the 3-all changeover. He grabbed the next three points to put himself a single point from winning. But Sandgren failed to close the deal at 6-3 ... or at 6-4 ... or at 6-5 ... or at 7-6.

“Got to get lucky sometimes, I’ll tell you that,” Federer said. “Because in those seven match points, you’re not under control.”

On Federer’s own second chance to take that set and force a fifth, Sandgren hit a ball that landed near the baseline. Federer thought it might be out — he turned to look at a line judge for a call that never came — yet barely flicked it back in a defensive manner, and Sandgren’s overhead smash went long.

Federer wagged his right index finger overhead — the universal sign for “I’m No. 1!” — and was on the right path. He ended the victory with a service winner at 192kmph, a little more than an hour after first staring down defeat.

The day started off in terrific fashion for the Swiss maestro as he broke the hard-hitting Sandgren early before taking the first set 6-3.

However, the problems began to surface for Federer in the second set, with the American taking it 6-2. Federer became unhinged by his standards in the third set, barking at chair umpire Marijana Veljovic over a contentious code violation.

In the midst of his heated moment, Federer was fighting soreness in his groin, which left him increasingly unable to get any real lift on his own serves as well as impeding his movement around the court.

However, in the fourth set, Federer looked revitalised and began to get some more zip back on his serves.

And after Sandgren blew his golden opportunity in the fourth set, Federer, having received treatment for his groin injury, dug deep into his reserve, using all of his experience to eventually break the American to close the deciding set out 6-3.