Federer looked to be on the verge of a shock exit but held on to defeat American Sandgren and reach the semi-finals in Melbourne for the 15th time in his career.
The 38-year-old became the first player to book his place in the men's last four, where he'll face Novak Djokovic following his 6-4, 6-3, 7-6 (1) quarter-final win over Milos Raonic.
Ashleigh Barty defeated Petra Kvitova 7-6 (6), 6-2 to continue her quest for glory on home soil, beating her previous best performance at the Australian Open.
She'll face Sofia Kenin in the last four after the 14th seed defeated Ons Jabeur 6-4, 6-4.
Tuesday's Quarter-Final Results
(2) Novak Djokovic bt. (32) Milos Raonic: 6-4, 6-3, 7-6 (1)
(3) Roger Federer bt. Tennys Sandgren: 6-3, 2-6, 2-6, 7-6 (8), 6-3
(1) Ashleigh Barty bt. (7) Petra Kvitova: 7-6 (6), 6-2
(14) Sofia Kenin bt. Ons Jabeur: 6-4, 6-4
Visit the Australian Open website to see the full results.
UK Replay Schedule (Time GMT)
Eurosport 1 at 1:19 p.m., 4:18 p.m. 6:18 p.m., 8:18 p.m. and 10:18 p.m.
Eurosport 2 at 3 p.m., 7:26 p.m. and 8:41 p.m.
Live Stream: Eurosport Player (UK)
U.S. Replay Schedule (Time ET)
ESPN 2 at 2 p.m. and 9 p.m.
Tennis Channel at 11 a.m. and 10 p.m.
Live Stream: Tennis Channel Everywhere (U.S.)
Federer failed to produce his best at Rod Laver Arena, but the Swiss star survived a huge scare to beat world No. 100 Sandgren to a semi-final spot as he pursues a seventh Australian Open title.
Sandgren forced three match points while leading 3-6, 6-2, 6-2, 5-4 in a tense fourth set and failed to convert another four times after leading by as much as three points in the tiebreak.
Durability also became a concern for Federer, who credited good fortune as a factor in his post-match interview:
The 20-time Grand Slam champion can expect the level of competition to increase in the semis, although tennis writer Nick Nemeroff highlighted Federer's evergreen qualities at major tournaments:
Djokovic overcame the challenge of Raonic in confident fashion despite the Canadian's best attempts to keep pace with his opponent on Rod Laver Arena.
It was a clinical display from the defending champion, who made Raonic look ordinary in a performance that underlined his potential to win back-to-back Australian Open titles for a third time in his career.
Djokovic couldn't ask for a much more difficult semi-final test than Federer, with the pair set to celebrate a half-century of matchups, per Gracenote Olympic:
Barty's hope for a home Grand Slam win in 2020 remains alive after she bested Kvitova in straight sets, earning redemption against the player who knocked her out at the same stage at last year's Australian Open.
The 23-year-old's triumph over the seventh seed also cemented her place among Australia's modern greats, per WTA Insider:
WTA Insider @WTA_insider
World No.1 Ashleigh Barty is the 1st 🇦🇺woman to reach an #AusOpen semifinal since Wendy Turnbull in 1984, who was also the most recent finalist in 1980. The last Aussie champion was Chris O’Neil in 1978. Barty defeats Kvitova 76(6) 62 and faces Kenin in the semis. https://t.co/6f3Q83mRVE
She'll meet a fellow rising prospect in Kenin, 23, who continued her career-best Grand Slam run in Melbourne following her own straight-sets victory against Jabeur.
Tunisian star Jabeur was one of only two unseeded players in the women's quarter-finals—Garbine Muguruza is the other—but Kenin's father, Alexander, didn't underestimate the task, per The National's Reem Abulleil:
Reem Abulleil @ReemAbulleil
Kenin's dad/coach Alexander: She played a very talented girl w a very unique playing style. I’m very proud of her that she found a way to handle it. Because it’s not very easy and it’s completely out of the box. This girl has everything, all the shots that other girls don’t have
Kenin will feel well-acquainted with Barty after the pair met on four separate occasions in 2019, though their head-to-head record leans heavily in favour of the Australian:
Barty will be the first seeded opponent Kenin has faced in Melbourne despite reaching the penultimate round, where the pressure of reaching a first Australian Open final could become a burden for either player.