It was the second consecutive Olympic title in the sport for Argentina, which became the first country in 40 years to repeat as champion. Hungary won gold medals at the 1964 and 1968 Games in Tokyo and Mexico City.
After losing to Nigeria in the 1996 final to Nigeria, Argentina failed to qualify for the Olympic tournament in Sydney. Since its return to the Games in 2004, Argentina's record is 12-0.
"The feeling we have is incredible," said Argentina captain Juan Riquelme. "I hope our country is celebrating back home. It was a beautiful day from the start."
Argentina recorded its fourth shutout of the Olympic tournament, including a 3-0 rout of Brazil in the semifinals.
Di Maria and Argentina star Lionel Messi, who had teamed up to produce the winning goal in overtime against the Netherlands in the quarterfinals, did so again for the only score Saturday.
Messi sent a long pass to Di Maria down the left side, setting up a one-on-one chance against Nigerian goalkeeper Ambruse Vanzekin. The goalie charged off the line, but Di Maria looped a shot over his head and into the net.
Because of the hot and humid conditions, the game was stopped in the 30th minute, almost unheard of in soccer, to allow a short water break.
Brazil had won the bronze medal Friday with a win over Belgium.