Roger Federer of Switzerland returns a shot to Gael Monfils of France during their quarterfinal men's singles match at the 2014 US Open tennis tournament in New York, Sept 4, 2014. [Photo/Agencies]

Gael Monfils of France leaves the court after losing a five set match to Roger Federer of Switzerland following their quarterfinal men's singles match at the 2014 US Open tennis tournament in New York, Sept 4, 2014. [Photo/Agencies]

NEW YORK - This is what ran through Roger Federer's mind as he stood one point from losing to Gael Monfils in the US Open quarterfinals:

"You got the back against the wall and hope to get a bit lucky. And you hope to play exactly the right shots that you need," Federer explained. "Or that he completely just messes it up. Either way works, as long as you get out of it."

Federer got out of it. Twice.

Steady as ever, even at 33, Federer saved two match points en route to coming all the way back from a two-set deficit, edging the 20th-seeded Monfils 4-6, 3-6, 6-4, 7-5, 6-2 on Thursday night to reach the semifinals at Flushing Meadows for the first time since 2011.

Frustrated by the Frenchman's unpredictable style, flummoxed by the swirling wind, and missing shots he normally makes, Federer was on the verge of defeat while trailing 5-4 in the fourth set.

The 17-time major champion's mind was racing.

"That is a very frustrating moment to be in. Being down match point, it's just not fun, because you're so close to leaving the court, head hanging down and ... going to take a shower and going to have to do press and all that stuff, which is so annoying after you've lost," Federer said.

"It's hard to block it out, (but) you snap right back in, because you don't have that much time," he continued. "You're like, 'OK, let me try and hit a good serve. Let's hope it works, because I don't want to hit a second serve.' All that kind of stuff. ... I have to face it and embrace it."

That he did.

With Federer serving at 15-40, Monfils had an opening for a backhand passing shot, but it flew long. At 30-40, Federer produced a forehand winner, and the crowd roared. Two points later, it was 5-all, and then Monfils double-faulted twice in a row to get broken.

Everything had changed, putting Federer on course to winning for the ninth time after dropping the opening two sets of a match.

"It came quick," said Monfils, who said he felt physically and mentally drained late.

"It's a matter of five minutes," he said. "I think I was down (for) five minutes. Roger just (jumped) on me."

Afterward, Federer credited the raucous support he heard in Arthur Ashe Stadium, saying the spectators "definitely got me through the match."

"It grows your belief that you can hit better shots, you can dig out more tough balls, you can serve better. All that just helps solidify your belief," Federer said. "I must say tonight was actually quite emotional for me."