The married young man and a single woman in Kunduz province's Dasht-e-Archi district were planning to run away after being prevented from marrying.
The woman, Sadiqa, 20, was engaged to another man, said Kunduz provincial police chief, General Abdul Raza Yaqoubi.
She and the man, 28-year-old Qayum hid in a friend's house, intending to make their escape. They were discovered by the Taliban on Sunday and stoned to death in front a crowd of about 150 men.
Amnesty International said it was the first confirming stoning in Afghanistan since Taliban rule was ended by the 2001 invasion.
When the Islamist extremists ruled Afghanistan, public killings for violations of their harsh interpretation of the Koran were common.