Nadal, the men's world number one and defending champion, needed a fifth-set tie-break to end the challenge of ninth-seeded Thiem, winning 0-6, 6-4, 7-5, 6-7 (4-7), 7-6 (7-5) in a match lasting nearly five hours and finishing around 2:00am (local time).
Twenty-four hours after Roger Federer fell to John Millman, his old rival avoided following him out of the tournament, but only just, completing a 0-6 6-4 7-5 6-7 (4/7) 7-6 (7/5) victory at 2.03am USA time.
Earlier the 36-year-old Williams, who is bidding for a record seventh title at Flushing Meadows as well her 24th major singles crown, started sluggishly in the night session, allowing Pliskova to take a 3-1 lead in the opening set before rebounding to win 6-4, 6-3.
When asked if he suffered during the match, Nadal said: "That's the right word".
Where can I get tickets for Rafael Nadal vs Dominic Thiem? . Thiem collected 24 of the opening set's 31 points, thanks in large part to a 13-3 edge in winners.
"I just play them instinctively, and that's how they work, or don't work sometimes."He came within two points of victory late in the fourth set before being pushed to a fifth, where he was two points from a loss. "I fight until the end, so it's always was question of a little bit of luck at the end". "Keep going", the victor said of the embrace. "Top person, sorry for him, but I'm sure he will have his chances in the future without a doubt".
"I am playing a lot of hours on this handsome stadium, that does not bother me - it just bothers my legs", he said. The way it ended up in the fifth set tiebreaker, from there it's 50-50.More news: Kavanaugh speaks at confirmation hearing
The Spaniard recovered from losing the first set 6-0 but admitted the toss of a coin could've won the tie-breaks. This set lasted 67 minutes but the real drama was just around the corner in set number four, with 12 break points in total and more than 80 minutes required to be completed!
The popular third seed will now attempt to take a step he has not managed since winning his only grand slam title here nine years ago and reach another final.
Nadal will now face Juan Martin del Potro in the semi-finals after the Argentine giant defeated John Isner in four sets. "But in few days I will look back and will remember how great it was to play in front of a packed Arthur Ashe - this great match".
This was only the fourth time in 282 career Grand Slam matches that Nadal has been bagelled in a set - on the three previous occasions, he lost.
"To reach the semifinal again here in NY in my favourite tournament is very special to me", said Del Potro after his eighth win over Isner in 12 meetings.
Thiem also remains the only member of the top 10 that Nadal has never tackled on a hard court.
He then rallied past Taylor Fritz 3-6 6-3 7-6 6-4 before beating 2017 finalist Kevin Anderson in straight sets 7-5 6-2 7-6. I didn't want to come back out'.
"We fought the whole match and I survived with my serve which was key".