Fifty sheep were stolen from a farm in Ammanford and the farmer spotted a flock two weeks later at a livestock market in Llanybydder.
After the ewes gave birth, paternity tests revealed they were the offspring of the farmer's rams.
Andrew Thomas, 39, of Garnant admitted handling the stolen sheep.
He will be sentenced at Swansea Crown Court this month.
Dyfed-Powys Police said this was the first time DNA evidence has been used in a case of this type in Wales, and only the third time across Wales and England.
Insp Matthew Howells said: "Traditionally, sheep rustling cases are very difficult to detect and prosecute, with this case being no exception.
"Although we were unable to prove who stole the sheep, we were able to use forensic techniques usually reserved for humans to help prove that the sheep were in fact the stolen ones."
A Carmarthenshire sheep rustler has been convicted after police used DNA testing on lambs for the first time in Wales.