The games only goal was scored against the run of play in the 13th minute by John O'Flynn.
After that Derry created chance after chance but couldn't get the equalising goal they deserved.
Derry stay 6th in the table and travel on Monday night to play Drogheda United.
Cork who will be delighted to leave Derry with the full haul points remain four points behind the leaders Dunddalk.
After the game Martin Holmes spoke with Cork Manager John Caulfield and firstly Derry boss Peter Hutton.