Di Maria, guilty of a remarkable double penalty-miss in a group game against Serbia, broke clear of the Nigeria defence and clipped the ball over Ambruse Vanzekin in the 58th minute.
Wilting in the searing heat, the Argentines survived a torrid half hour of Nigerian pressure to cling on for victory.
The mid-day showdown at the Bird's Nest was a repeat of the 1996 final, which Nigeria won 3-2 to become the first African team to win the tournament.
The Olympic soccer tournament is restricted to under-23 teams with each allowed to field up to three over-age players.
The first half was played at walking pace and there were no clear cut chances before a much-needed water break on the half hour.
Peter Odemwingie created Nigeria's first opening shortly afterwards when he broke down the left and sent a low ball across the face of the goal but Promise Isaac just failed to make contact.
Di Maria then produced Argentina's first real effort with an out-swinging 25-metre shot which was turned away by Vanzekin.
Vanzekin also had to be quick to dive at the feet of Sergio Aguero after he was set free by an incisive Lionel Messi pass after the restart.
Messi then had a shot fisted away by Vanzekin before setting up the goal.
The Barcelona player slipped a pass to Di Maria who broke clear on the halfway line and beat Vanzekin with an exquisite finish.
Nigeria sprang to life as Victor Obinna had a shot saved by Sergio Romero and Nicolas Pareja saved Argentina by blocking Victor Anichebe's effort after Promise Isaac pulled the ball back from the byline.
Argentina escaped again when an attempted clearance hit Ebenezer Ajilore and ricocheted centimetres wide of the post and an inswinging cross from Obinna was missed by two Nigerian forwards.
Nigeria were agonisingly close when Anichebe's close-range effort was saved by Romero at the second attempt.
In between, Messi was foiled by a last-ditch tackle from Apam Onyekachi.