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.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."