The reigning US Open champion and world number one endured a gruelling match against ninth-seeded Thiem, who swept the first set 6-0 on Tuesday night, reports EFE news agency.
Nadal mounted an impressive comeback, winning the next two sets as he got to grips with the Austrian's power.
Thiem levelled the match with a fourth set tie-break victory before Nadal finally edged a tense final set after another tie-break.
The match, which lasted 4 hours and 49 minutes, ended after 2 a.m. local time, with Nadal prevailing 0-6, 6-4, 7-5, 6-7 (4-7), 7-6 (7-5).
The Spaniard moves on to the semi-finals where he will meet Argentine Juan Martin Del Potro.
Del Potro is headed to the US Open semi-finals for the third time after defeating US player John Isner 6-7 (5), 6-3, 7-6 (4), 6-2 here on Tuesday in a match that lasted more than 3 1/2 hours.
While both men suffered in the heat -- more than 90 F (32 C) -- and humidity at the Arthur Ashe Stadium, the No. 3 seed coped better than Isner, who was trying to become the first American in 12 years to reach the US Open semis.
And though the home court advantage was theoretically Isner's, the crowd included a large number of vocal supporters of the Argentine.
"An epic match. We're both tired in the end," Del Potro said afterwards.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
