The Barcelona forward hit the frame of the Paraguay goal twice before scoring from a free kick in the 64th minute at the Mario Kempes stadium in Cordoba.
"This triumph is very valuable," said Messi. "Now we go to Peru, who are a very difficult team to play against.
"Leading the group is the least important aspect. The key is to keep gaining confidence as a group."
Argentina are currently top of the CONMEBOL standings with 13 points from six matches, just one point ahead of both Chile and Ecuador.