The winner of the repechage final will join hosts England, Australia, Wales and Fiji in Pool A.
Flyhalf Felipe Berchesi scored 11 points with a try and two penalties and scrumhalf Agustin Ormaechea 12 from four penalties as Uruguay crushed their opponents in the second half after changing ends 6-3 up.
Uruguay wore their opponents down with superior forward play and punished infringements by converting the majority of their penalties.
Berchesi and openside flanker Diego Magno ran in Uruguay's two tries in the final seven minutes.
"We had trouble with our lineouts because of a lack of height and physique but I think we held the ball more," Uruguay hooker and captain Nicolas Klappenbach told reporters.
"Most of them are sevens players, who often tried to intercept our moves. We decided to carry the ball more and fight in the scrums."
(Writing by Rex Gowar; Editing by Peter Rutherford)
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