Leading 5-4 in the tiebreaker, Thompson put a routine backhand into the net and then double-faulted. The eighth-ranked Zverev put away the match with a cross-court forehand that the 75th-ranked Australian couldn't handle, winning 4-6, 6-3, 7-6 (5) on Wednesday.
Zverev, a 20-year-old German, is a winner of three titles this year, two of them on clay.
"I'm just happy to get through that one. Seven-to-six in the third is always something very nice," Zverev said. "You feel good about yourself. Hopefully I can do it better the next match."
Tenth-ranked Milos Raonic of Canada, who beat Zverev in the fourth round of Wimbledon this year, also advanced, defeating Nicolas Mahut 7-6 (2), 7-6 (8). Raonic, the 2014 Citi Open champion, next faces veteran Marcos Baghdatis. They haven't played each other in five years.
The Citi Open is a hard-court tuneup for the U.S. Open, which starts Aug. 28.