The U.S. will play defending champion Russia for the title Nov. 30-Dec. 3, with the Americans hosting the final for the first time since 1992. Russia defeated Germany 3-2 in the other semifinal in Moscow.
The Americans, who have won the most Davis Cup titles (31), last won in 1995.
After Roddick reeled off 16 aces to leave the U.S. ahead 3-1 in the best-of-five series, James Blake beat Simon Aspelin 6-1, 6-3 in a shortened finale to make the score 4-1, indystar.com reports.
"If you would have told me I could get through three sets with Jonas without getting broken, I would have questioned your sanity a little bit," Roddick said.
Mikhail Youzhny and Igor Andreev won four-set matches to give Russia a 3-2 victory in the best-of-five series in Moscow. Germany had taken a 2-1 lead by winning yesterday's doubles after the sides split the singles matches three days ago.
Andy Roddick beat Jonas Bjorkman 6-2, 7-6 (7-3), 6-4 to clinch the U.S.'s 4-1 win over Sweden in Gothenburg. Roddick's victory gave the U.S. a 3-1 lead and guaranteed a first final appearance since 2004.
Youzhny beat Philipp Petzschner 6-4, 6-4, 3-6, 6-3 in the first match to pull Russia even in the series. Igor Andreev then clinched Russia's fifth trip to the Davis Cup final with a 6-3, 3-6, 6-0, 6-3 win in two hours 39 minutes over Philipp Kohlschreiber.
Russia's Nikolay Davydenko was to face Tommy Haas in the first singles match but both were unable to play because of illness, the Davis Cup Web site said. Youzhny and Petzschner were then selected.
Roddick scored two service breaks in winning the first set. Both players held serve in the second to force a tiebreak, in which Roddick took the first five points.
Roddick broke for a 3-2 lead in the third set and served out for the victory at 5-4. James Blake defeated Simon Aspelin 6-1, 6-3 in the final match, which was shortened to best-of- three with the series outcome already settled., Bloomberg reports.
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