Roger Federer, at age 38, showed Tuesday that he still has some magic left.

The 20-time Grand Slam champion saved seven match points, all of them in the fourth set, and rallied for a 6-3, 2-6, 2-6, 7-6 (8), 6-3 win over the United States' Tennys Sandgren in the quarterfinals of the Australian Open.

It was the second consecutive match in which Federer performed a great escape. The tournament's third seed captured the last six points of a fifth-set tiebreaker against Australia's John Millman to win 4-6, 7-6 (2), 6-4, 4-6, 7-6 (8) on Sunday.

"I was incredibly luck today, tonight, I don't even know what time it is," Federer said in an on-court interview after topping Sandgren, who is ranked No. 100 in the world. "I'm lucky to be here, and I might as well make the most of it."

With Federer serving at 4-5 in the fourth set, Sandgren had three match points, but Federer managed to hold serve.

The set then went to a tiebreaker, which was tied 3-3 after six points. As the players changed ends, a ballgirl ran hard into Sandgren's right leg. However, Sandgren won the next three points to set up three match points, all of which he dropped.

He got one more match point at 7-6, but Federer stayed alive again. Federer finally closed out the tiebreaker on his second chance, at 10-8.

The only service break of the final set came in the sixth game, with Federer never facing a break point in the set.

Next up for Federer is a semifinal matchup against either second-seeded Novak Djokovic of Serbia or 32nd-seeded Milos Raonic of Canada.

Sandgren, a 28-year-old Tennessee native, fell short in his bid to become the first American man to reach the Australian Open semifinals since Andy Roddick in 2009.