Roger Federer’s rally sets up Saturday’s semifinals

Steady as ever, even at 33, Federer saved two match points en route to coming 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 . . . 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.’’

Monfils, 28, was trying to reach his second career Grand Slam semifinal. Instead, Federer advanced to his 36th, ninth at Flushing Meadows. Five of Federer’s major titles came at the US Open from 2004-08, but he lost in the quarters in 2012, and the fourth round in 2013.

On Saturday, the second-seeded Federer will play 14th-seeded Marin Cilic of Croatia. The other semifinal will be No. 1 Novak Djokovic against No. 10 Kei Nishikori.

It took Monfils 78 minutes to build a two-set lead, shaking off a twisted right ankle that left him down on the court. It helped that Federer made 26 unforced errors in that span.

And as if all he had to do was want to improve his play, Federer did. He suddenly was remarkably cleaner, with only one unforced error in the third set, and two in the fifth.

Attacking the net helped: Over the final three sets, Federer earned the point on 34 of 46 trips forward.

‘‘I knew I could play better after the first couple of sets,’’ Federer said. ‘‘I believed I could turn it around from the get-go when the third set started.’’

Monfils is nothing if not unpredictable. In an era where some men, including Federer, have two coaches, Monfils goes without any. He'll admit to tanking points, games or entire sets. He sips sodas during matches, including Thursday. He'll go for a between-the-legs shot when a mundane forehand would do.

Make no mistake, though. This was not easy. The turnaround might not have been possible for Federer a year ago, when he was dealing with a bad back and trying to figure out whether he should switch to a larger racket head.

But now Federer, however old, is approaching his skills of old. He got to the finals at his previous four tournaments — including a loss to Djokovic in Wimbledon’s title match in July — the first such run by a 30-something since Ivan Lendl in 1990. One more victory, and Federer’s final streak will stretch to five in a row.

Mirza and Soares had each been successful mixed doubles players, so Mirza said during the trophy presentation that she wasn’t sure why it took them this long to pair up.

‘‘I tried to play with Sania for a long time,’’ he said later.

‘‘What a lie,’’ she interjected.

‘‘She finally gave me a chance to play,’’ he insisted.

Mirza has now won three Grand Slam mixed doubles titles. Soares was the 2012 US Open champion with Ekaterina Makarova, who lost to Serena Williams, 6-1, 6-3, in the singles semifinals. Soares joked that this means Mirza will reach the singles semis in in two years.

In the super tiebreak, Mirza and Soares went ahead, 9-4, before Spears and Gonzalez won five straight points. They clinched on their sixth championship point.

Give Tomas Berdych credit for this: He apologized.

Sure, it came a day after his rant at a chair umpire over what turned out to be a correct call in Berdych’s quarterfinal loss. And sure, it came via Twitter, instead of face to face.

The player from the Czech Republic extended an olive branch by writing a tweet that said: ‘‘this is my personal apologize to the referee from yesterday.She was right.My emotions were driving my crazy...Sorry for that.’’

In the third set Thursday against Marin Cilic, the sixth-seeded Berdych thought he won a point when he raced forward to get to a ball and lift it back over the net. But chair umpire Louise Azemar Engzell awarded the point to Cilic, saying the ball bounced twice before Berdych hit it.

Berdych argued over and over, at one point saying: ‘‘Have you ever had a racket in your hand?’’