Heinze scored with a diving header in the sixth minute from 12 yards from Juan Sebastian Veron’s corner at Ellis Park.
Argentina striker Gonzalo Higuain shot wide from seven yards in the fourth minute when Lionel Messi dribbled past several defenders before squaring to his teammate.
Enyema made a one-handed save from Messi’s sixth-minute shot from outside the box, and Messi missed from close range in the 48th.
Chinedu Obasi had Nigeria’s best chance, shooting wide from a tight angle in the fourth minute.