Second seed Thiem beat Russia's Daniil Medvedev 6-2, 7-6 (9-7), 7-6 (7-5), while Zverev fought back from two sets down to overcome Pablo Carreño Busta of Spain 3-6, 2-6, 6-3, 6-4, 6-3 on the Arthur Ashe Stadium court.

Both players will be aiming to win their first Grand Slam title in Sunday's (September 13) final, which will also see the crowning of the first men's male major singles champion born in the 1990s.

Zverev, the fifth seed, looked to be staring semi-final defeat in the face when Carreño Busta raced into a two-set lead.

The Spaniard was in superb form and appeared to have moved to the brink of progressing to the final until Zverev mounted a valiant fightback.

Zverev stepped up a gear in the third and carried that into the fourth set to force a decider.

The world number seven proved too strong for Carreño Busta in the fifth, closing out a battling victory which saw him come from two sets down to win for the first time in his career.

"I knew I had to come up with better tennis and be more stable," said Zverev.

"I knew I had to play better. 

"I've never come back from two sets to love but I'm happy to do it at this stage.

"I'm through to my first Grand Slam final and that's all that matters."

In the second semi-final, Thiem put in a classy display in a high-quality encounter with Medvedev, last year's runner-up.

The Austrian won the first set following a contentious decision when the umpire did not acknowledge an attempt to challenge a call from Medvedev, who was given a code violation.

It appeared to rattle the Russian, who lost the game and was then broken again at 5-2 to hand Thiem the opener.

Thiem, the world number three, claimed sets two and three on a tiebreak to join Zverev in the final.

"It was definitely anything other than a routine three-set win," said Thiem.

"The first set I got a bit lucky with this strange situation [Medvedev's failed challenge].

"After that it was great tennis from both of us and I could easily have been two sets to one down."