That put the United States on the medal stand along with more traditional curling powers Finland and Canada, who play later Friday for the championship.
Britain was shut out of a medal one Olympics after Scottish housewife Rhona Martin threw the "Stone of Destiny" to win the gold medal in Salt Lake City. David Murdoch's team is also from Scotland, which is considered the birthplace of curling.
With the Americans holding the big last-rock advantage known as the hammer for the final end, or inning, they played defensively and kept the British from building any protection. Murdoch had one rock in the target area, and he put his last rock out front as a guard.
But Fenson, a Minnesota pizzeria owner, had an open draw around the right to get inside of Murdoch's rock and give the U.S. the bronze.
The Americans took control with three points in the third end and made it 6-2 with a pair of points in the sixth. But the British rallied with three points in the seventh end when Murdoch knocked out an American rock and left his in the scoring zone, along with two others.
Britain's best chance to win came in the ninth, when it held the big last-rock advantage known as the hammer. But it could only manage one pointessentially holding serve.
The hammer went over to the Americans in the 10th end, and they used it to set up the winning shot.