Backed by a boisterous home crowd, Berdych jumped to an early lead, converting the only break point of the first set in the seventh game as the two hard-serving players battled from the baseline.
But Roddick used breaks early in both the second and third sets to take control of the match as Berdych suffered with leg cramps that needed medical attention.
Both players held serve through the fourth set but Roddick opened the tiebreak with a breathtaking backhand service return for a mini-break and he rolled from there to take the match.
The U.S., who last won the trophy in 1995, will face Spain in the quarter-finals after the Spaniards went 3-1 up against Switzerland, playing without world number one Roger Federer, with one rubber remaining in their tie in Geneva.
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