The top-seeded Isner lost to Brown in the second round of the U.S. Men's Clay Court Championship on Wednesday night.
It was Brown's first career victory against a top-10 player. The German closed out a 6-4, 6-7 (7), 7-6 (4) win with a forehand winner.
"I've had a lot of matches where I've played good tennis, where I was close, and you've just got to keep playing," Brown, 29, said. "I've got to play my tennis. If I start playing the tennis (the opponent) wants, that's not good for me.
"He's been in these situations much more often than me -- I got a little tight in the second set, maybe at the end of the third -- so I had to try to keep playing. It feels unbelievable."
The 6-foot-5 Brown, who dropped each of his previous three matches against opponents ranked 10 or higher, has spent most of his career on the Challenger circuit, where he has won five titles.
Isner, ranked No. 9, was the defending champion in Houston. He had 13 aces in the loss.
The 6-9 Isner apologized following his postmatch interview to a tournament official for a "pathetic performance -- I'm sorry you had to see that."
"I just didn't feel it tonight," he said.