Setting a men's record with his 71st Grand Slam appearance (breaking a tie with Fabrice Santoro), Federer hung on to win his return to the US Open, as well as his first match ever under the roof on Arthur Ashe Stadium.
The teenager faced Federer for the first time in his career in the second round of this year's Miami Open and took the Swiss to a first-set tiebreak before losing 7-6 (2) 6-3.
"He is a great player and has a bright future ahead of him", he said of the 19-year-old. I was anxious about the back injury.
"I had a slow start".
On Wednesday, Tiafoe stunned the five-time US Open champion 6-4 in an aggressive first set.
But Swiss, who blamed his early struggles on not being able to prepare as he would have liked, dismissed suggestions he was having issues with the back injury that troubled him heading to NY.
"I was maybe a bit anxious from the beginning with my back issue, but eventually I was able to let go", said Federer. "I'm very happy that I'm feeling as good as I'm feeling right now", Federer said.
"I'd hit against the wall by myself, mimicking techniques I had seen older boys at the academy do".
Federer insisted his back has recovered, saying: "To get through a five-setter you have to be okay somehow".
"I was definitely also lucky to play tonight because the rain". So that would have been tougher for me maybe to back it up back-to-back days.
"At the end I'm going to try to focus on my own game like I usually do and make sure I make it tough for Frances to get through me". I still believe that.
He went through that tournament with a certain level of ease as well, only dropping a single set in his second match against David Ferrer.
One of America's biggest hopes, his inspiring story began when, as the son of immigrants from Sierra Leone, he spent his early years at the Junior Tennis Champions' Center in Maryland, where his father Constant was head of maintenance.
The 36-year-old Federer, whose capture of the Australian Open and Wimbledon titles in 2017 has taken his Slam count up to 19, is bidding for a record sixth crown in NY.
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