Carlos Tevez clinically tucked in a Mauro Rosales cross in the 18th minute of an ill-tempered South American clash dominated by Argentina before 44,000 at the Olympic Stadium.
It was the Boca Juniors playmaker's eighth goal of the competition for Argentina, who finished with a perfect record of six wins out of six, scoring 17 goals without reply.
Paraguay had Emilio Martinez sent off in the 66th minute for elbowing Andres D'Alessandro in the face and their misery was compounded seven minutes from time when Diego Figueredo was dismissed for a second bookable offence.
Argentina, runners-up to Nigeria in Atlanta eight years ago, had not won an Olympic gold in any sport since Tranquilo Capozzo and Eduardo Guerrero took the men's double sculls rowing title at the 1952 Helsinki Games.
Paraguay's silver was the first Olympic medal in the country's history.
However, they were completely outclassed by an Argentina side that could have won by four or five goals, Rosales and Tevez both coming close at the start of the second half.
Paraguay goalkeeper Diego Barreto pulled off a superb reaction save to keep out a Luis Gonzalez volley in the 60th minute.
Striker Cesar Delgado had shot cleared off the line in the 75th minute by Paraguay captain Carlos Gamarra, himself lucky not to have been sent off after elbowing Tevez in the first half.
Argentina became the first Latin American team to win the Olympic title since 1928, when they were beaten by Uruguay in the Amsterdam final.
For Argentina coach Marcelo Bielsa, the gold medal was vindication for sticking to an attacking 3-4-3 formation after their shock first-round exit at the 2002 World Cup.
More from rediff