Santa Cruz's team-mate, Miguel Benitez, and Peru's Andres Mendoza had both produced candidates for the miss of the tournament, squandering easy chances from point-blank range, before Santa Cruz ran onto a Roberto Acuna pass in the 88th minute to score the winner. The goal, his third in the tournament, made him joint top scorer alongside Brazil's Marcio Amoroso.
The Paraguay-Peru match was the second game in a Group A double bill in Pedro Juan Caballero. Bolivia and Japan played out a 1-1 draw, a result that saw both sides eliminated from the tournament.
Bolivia had needed a win to progress and appeared to be on their way after a 53rd-minute goal by Erwin Sanchez. Japan, who had accepted a special invitation to take part in the competition, did not look capable of replying until they won a 73rd minute penalty which was coolly converted by the Brazilian-born striker Wagner Lopes.
Bolivia finished third in Group A with two points, not enough to have a chance of going through as one of the two best third-placed teams. Chile, third in Group B, and Argentina, third in Group C, already have three points. The teams which now finish third in Groups B and C will go through automatically. Japan, who had needed a big win to have a chance of qualifying, picked up their first and only point.
With the top two in each group going through automatically, the Paraguay- Peru match was only to decide who finished first and second. Paraguay took top place having completed the first round without conceding a goal.
Elsewhere, Martin Palermo, the Argentina striker who missed three penalties in his country's 3-0 defeat to Colombia in Group C on Sunday, stayed in his hotel with his team-mates, refusing to speak to the media. Less shy was Javier Alvarez, the coach of Colombia. "We will hammer any team that does not defend well against us," he said.