The Manu trailed 15-0 early in San Sebastian but rallied to lead 21-20 at half-time.
Leading 29-27 with a minute to go Samoa conceded a penalty and first five Will Hooley converted from a difficult angle to secure a dramatic 30-29 win - the first for the USA in six tests against their men in blue.
Steve Jackson said his players were sound defensively and created more opportunities with the ball in hand but execution and decision making let them down.
