The sixth-seeded Czech won 6-1, 6-2, 6-4 in just 98 minutes at the U.S. Open on Tuesday, a day before Thiem's 21st birthday. The 45th-ranked Austrian was the only unseeded man among the final 16.
Thiem had 35 unforced errors and failed to convert all seven of his break points.
Berdych was 5 of 9. He faces 14th-seeded Marin Cilic in the quarterfinals.