The Americans came to Rio as favourites and were undefeated until Serbia knocked them out in a five-set upset on Thursday when the U.S. team lost its top scorer Foluke Akinradewo to a leg injury.
With their star middle blocker back on the court, the Americans beat the Dutch women 25-23 25-27 25-22 25-19 in the bronze medal match.
Akinradewo said some therapy on her left leg put her back in competition for the bronze medal game, as she shed a tear over missing another opportunity to capture the gold.
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"That's what we want, of course. No team comes here not wanting to win the gold," she told Reuters. "But this bronze is just as special for me because we were able to fight back from a disappointing loss. We were so close," she said.
The United States reached the finals in the two previous Olympics in London and Beijing, but were defeated by Brazil both times.
Serbia, competing for Olympic medals for the first time, will take on China, who are after their third gold in the final later on Saturday.
(Reporting by Anthony Boadle; Editing by Bill Rigby and Meredith Mazzilli)
