With the best-of-three series at 1-1, Robin Soderling and Robert Lindstedt edged Mikhail Youzhny and Dmitry Tursunov 4-6, 7-6 (5), 11-9 after saving a match point at 9-8 in the match tiebreaker.
Sweden also won the title in 1988, 1991 and 1995. Russia has never won it.
Soderling maintained his unbeaten record this week, winning all eight matches he played in singles and doubles. He is only the third player in the 31-year history of the event to achieve the feat, following John McEnroe of the United States in 1984 and Chile's Fernando Gonzalez in 2003.
Soderling began by overwhelming Youzhny 6-3, 6-1 in just 63 minutes, before Igor Andreev rallied to beat Thomas Johansson 2-6, 6-3, 6-4 to level the series.
Soderling broke to lead 4-2 in the first set when Youzhny hit a forehand long. He broke for a 2-1 advantage in the second set. Another forehand error then gave Soderling a further break for 4-1, and he broke again in the final game.
In the second match, Johansson sped to a 4-0 lead in the opening set. But Andreev's speed and powerful forehand began to turn the match, and a break for 3-1 was enough to secure the second set.
In the final set, Andreev broke for a 1-0 lead on a backhand error. Johansson held a break point to level at 4-4, but Andreev won the next two games.
"I didn't start 100 percent,'' Andreev said. "I was maybe nervous, but then the concentration started. I served better and found my game.''
Russia took the first set of the doubles and held a break in the second before Sweden leveled at 4-4. Lindstedt fought off a break point before holding for a 5-4 edge, and Sweden went on to win both tiebreakers.
The winners received $457,600 and the losers $300,000.
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