The World Cup semi-finalists took an early lead when defender Diego Lugano pounced on a lucky ricochet to steer home from close-range.
But Shane Long headed home an equaliser barely three minutes later.
Uruguay re-established their lead in the 22nd minute when Edinson Cavani finished with aplomb before the impressive Abel Hernandez slotted home in the 39th minute to give Uruguay a two-goal cushion.
