The twin brothers broke Youzhny's serve once in each of the first two sets to take a two-set lead before breaking Tursunov in the opening game of the third set to seal a comfortable victory in less than 90 minutes.
The win pulled the Americans back to 2-1 down in the three-day tie after Marat Safin and Youzhny had given the home team a 2-0 lead by winning both singles matches on Friday.
Safin overpowered Andy Roddick 6-4 6-3 7-6 while Youzhny prevailed over James Blake 7-5 1-6 6-1 7-5 to put Russia in command.
The Russians are seeking their first victory over the U.S. in Davis Cup after losing two previous ties, including the 1995 Moscow final on a similar clay surface.
The winners will face either Argentina or Australia, who meet in the other semi-final in Buenos Aires, in the December final.
NO PROBLEMS
The Bryans, who have won all four grand slam doubles titles including the French Open on clay in 2003, had few problems against the rarely-used Russian duo and they did not face a break point in the match.
"We just love to win a point for our team. It's always great to win for your country," Bob Bryan said.
"We had Andy and James coming up to us, saying 'Get us a chance, just give us another shot'," Mike added.
The Americans, who have now won nine of their 10 Davis Cup matches, broke Youzhny's serve in the eighth game of the opening set when the U.S. Open semi-finalist missed an easy smash on break point for a 5-3 lead. Bob Bryan then served out to love to clinch the first set in 27 minutes.
They broke Youzhny again in the seventh game of the second set and Bob put the U.S. two sets up with a powerful ace down the middle.
After Tursunov lost his serve in the first game of the third set, there was no coming back for the Russians.
"It's not that we played that bad. You have to talk about the other team playing so well," Youzhny said.
"They served exceptionally well today and just didn't give us any chances whatsoever."
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