Jessica Springsteen was part of the United States side which finished second behind Sweden in the showjumping team competition.
The 29-year-old secured a podium finish with team-mates Laura Kraut and McLain Ward after a jump-off for gold.
It proved a disappointing night for Great Britain, though, after their first two riders Holly Smith and Harry Charles had 24 penalties between them.
With the team way off medal contention, the decision was taken to withdraw Ben Maher’s individual champion Explosion W.
GB equestrian team leader Richard Waygood said: “Holly and Harry rode with great skill, but this is the pinnacle of Olympic competition, and with 24 faults Team GB will not be in the mix for a podium place.
“Ben and Explosion have shown their world-class calibre in winning individual gold, and we have collectively decided it is in the best interests to save Explosion for another day.”