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Argentina was satisfied with Di Maria's sixth-minute goal.
After a 1-0 win against Uruguay on Friday, Argentina will be qualified for next year's World Cup.
Angel Di Maria's victory secured victory and La Albiceleste was second in South American qualifying, after 12 games.
They will be facing leaders Brazil who were qualified on Tuesday by beating Colombia.
Uruguay is currently in sixth place, level with Chile (who occupy the final automatic qualifying spot), having lost three consecutive games.
If Uruguay, Colombia, or Chile lose, victory for Argentina is enough.
The hosts missed many chances, falling behind to Di Maria's curling efforts after he was fed on seven minutes by Juventus' Paulo Dybala.
Lionel Messi appeared for 15 minutes despite not being 100% fit. This ran the risk of disturbing Paris St-Germain, who he has yet to score a league goal.
Peru also won, defeating Bolivia 3-0 in Lima.
