Almirón was a driving force throughout for La Albirroja, with some exciting runs from a left wing position, but despite his best efforts Paraguay could not find a way through against Lionel Scaloni's men at Estádio Nacional de Brasilia.
Instead, Argentina booked their place in the quarter-finals on a night when Lionel Messi became his country's joint-most capped player of all time with his 147th appearance for La Albiceleste.
Unsurprisingly, he was involved in the goal, feeding Ángel Di Maria to set up Papu Gómez in the tenth minute, and while Paraguay had more of the possession and more shots on goal, that proved to be the decisive moment.
Almirón played the full game for Paraguay, who can still join Argentina in the last eight after beating Bolivia in their opening Group A game last week.
On Friday, they take on Chile before their final group fixture against Uruguay at Estádio Olímpico Nilton Santos in Rio de Janeiro on Tuesday, 29th June.