Roger Federer defied age and logic once again to save seven match points before beating unseeded American Tennys Sandgren in a sensational Australian Open quarter-final.
The out-of-sorts Swiss fought off form and fitness concerns before winning 6-3 2-6 2-6 7-6 (10-8) 6-3.
World number 100 Sandgren looked set to be the lowest ranked player to reach the Melbourne semi-finals since 1991.
But third seed Federer battled to win in three hours and 28 minutes.
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The 20-time Grand Slam champion, who had a medical timeout in the third set for a groin problem, will play Serbia’s defending champion Novak Djokovic or Canadian 32nd seed Milos Raonic in the last four.
Federer calmly raised his racquet in the air, taking the acclaim of a buzzing crowd on Rod Laver Arena, after Sandgren dumped a forehand into the net on the Swiss’ first match point.
The fatigued pair shook hands at the net, Sandgren wishing his rival luck before trudging off to a standing ovation from the 15,000 fans barely able to believe what they had seen.
“You’ve got to get lucky sometimes I tell you that,” Federer said. “Sometimes you’re not under control.
“I just hoped he wouldn’t smash a winner, just keep the ball in play and if he does miss one of two then see what is going through his mind.
“As the match went on I felt better and the pressure went away.
“I didn’t deserve this one but I’m standing here and I’m obviously very happy.”
Earlier Ashleigh Barty became the first Australian woman to reach the semi-finals at her home Grand Slam for 36 years with victory over Petra Kvitova in an absorbing encounter in Melbourne.
The top seed made 2019 runner-up Kvitova pay for a host of missed chances in a 7-6 (8-6) 6-2 victory at the Australian Open.
French Open champion Barty will face American 14th seed Sofia Kenin next.
Kenin reached her first major semi after a 6-4 6-4 win over Ons Jabeur.
The last Australian woman to reach the semi-finals in the singles at Melbourne Park was Wendy Turnbull in 1984, who was the most recent finalist from the home nation in 1980.
Eight squandered break points, one missed set point and a lost tie-break lead tell the story of what went wrong for Kvitova against Barty in the first set.
The Czech held five break points at 3-3 in a gripping game that lasted more than 10 minutes – having carved a 0-40 lead with two blistering forehand returns – but eventually allowed the Australian to hold when she netted a forehand return.
She had a mini-break in the tie-break but again enabled Barty to get herself back in it when she netted after a fantastic rally where the Australian was at her defensive best and getting on the end of everything the Czech threw at her.
Another netted forehand gave Barty a mini-break and Kvitova handed her the set when she went long with a backhand.
Kvitova, who was beaten in last year’s final by Naomi Osaka, swiftly left the court at the end of the set but when she returned she could not find a way back into the match as Barty raced to a 4-0 lead.
Where the gripping first set lasted one hour and nine minutes, Barty needed just 35 minutes in the second. She was halted only by a dropped serve in the sixth game but went on to seal victory with an ace.
“It’s been absolutely incredible,” said Barty, who is seeking to become the first Australian women’s singles winner since Chris O’Neil in 1978.