Nadal could easily have taken a firm control of the rest of the set with Thiem’s hopes shattered.
But instead Thiem overcame the problem to win a thrilling tiebreak.
Federer spoke about the demons in his head after he came back from 8-4 down in the fifth-set tiebreak against John Millman last week.
And Thiem reckons he had to fight the same mental battle as the world No 3.
“It’s a little bit demons in the head like Roger said,” Thiem explained. “It’s true everybody has it.
Rafael Nadal’s wife watches on anxiously during Dominic Thiem showdown
“I was rushing way too much and changing my tactics which was wrong. It was tough to handle at 5-5 against Rafa.
“You have to deal with these situations almost every single game. I am very happy I won the tiebreak otherwise I would be in a fifth set.
“I just wanted to stay in the match and then I got the break. It was a special situation for me serving for the match against Rafa for my first semi-finals here.
“It was a mentally tough situation and I couldn’t handle it but I turned it around in the tiebreaker.”
“We already had this epic match in New York two years ago and today I felt I was lucky in this situation.
“The net cord was on my side but that is necessary because he is one of the biggest legends of all time so you need some luck to beat him.
“I am feeling good so far but I am full of adrenaline. We will see when that is off how I feel tomorrow.”
