The Liverpool midfielder notched the winner 12 minutes from time with a well-placed shot into the bottom corner after capitalizing on a poor clearance by Paraguay defense.
The 100% record put Argentina on top of Group C with nine points, three ahead of second-placed Paraguay.
Argentina had some changes in their starting line-up as their qualification to the quarter-finals was guaranteed.
They struggled to create scoring opportunities in the first-half but became more dangerous in the second period.
Argentina's best chance came seven minutes after the break when Rodrigo Palacio's powerful shot struck the post.
In the other Group C game, Jaime Castrillon's 15th-minute header earned Colombia a 1-0 win over the United States.
Colombia, who are eliminated from the competition, finished third in the group with three points while U.S remained at the bottom having failed to grab any win.