The Eagles, who had qualified for all but one of the previous six World Cups, followed up their 27-22 win in last weekend's first leg in Montevideo with a more comfortable win.
Uruguay, who played the last half hour a man short after prop Mario Sagario was sent off, get a second chance to qualify for the World Cup through next year's play-offs.
As in the first leg, the Eagles ran in four tries only this time Uruguay failed to make the late response that saw them recover from a similar 27-6 deficit last weekend.
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Tries by flanker Louis Stanhill and wing Kevin Swiryn, who scored two in Montevideo, helped the US to a 13-3 lead at half-time.
Captain Todd Clever made an interception and ran 35 metres to score the third try early in the second half before Sagario was shown the red card.
The Uruguayans fought to get back into the game making light of their numerical disadvantage before flanker Clever scored another try in the dying seconds.
US fly-half Mike Hercus (pictured) kicked one conversion and one penalty, while Uruguay fullback Jeronimo Echeverry, who scored 19 points last weekend, replied with two penalties.
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