Guilty as Charged (Hadith No. 2005)

Bismillah.

Volume 3, Book 38, Number 508 :
Narrated by Zaid bin Khalid and Abu Huraira (radiallaahu `anhu)
The Prophet (sallallaahu `alayhi wasallam) said, “O Unais! Go to the wife of this (man) and if she confesses (that she has committed illegal sexual intercourse), then stone her to death.”

In Muslim (1698), there’s an addition to this narration:

“..He said: I went to her the next day and she admitted it, so the Messenger of Allaah (peace and blessings of Allaah be upon him) ordered that she be stoned.”

The evidences to charge one with guilt are only three according to Islamic Shariah. They are testimony of witnesses, confession, and taking an oath.
A judge of Islamic Shariah is not allowed to carry out the legal punishment (Hudood) without having the legal evidence to prove guilt of the accused.
However, it is liable for a judge in an Islamic court to punish a person just to discourage further criminal behavior when there are indications of his criminality, if it is useful.

Who should carry out the hadd punishment for zinaa (adultery)? Read on it here.