The American team will play for the title in November against Italy, which eliminated the defending champion Russian team 4-1 in the other semifinal at Castellaneta Marina, Italy.
Huber and Mattek-Sands won their match against Kveta Peschke and Iveta Benesova at Brno in the Czech Republic 2-6, 7-6 (7-2), 6-1.
"I'm speechless," Huber said. "Kveta is just the best player (and) we were kind of stunned, we just couldn't get the ball away from her. But in the end we were in control of the match."
Earlier, the U.S. team's Alexa Glatch had evened the best-of-five competition at 2-2 with a 6-2, 6-1 rout of Petra Kvitova.