However, Derry were considered deserving of the victory despite the fact that their killer second goal came courtesy of a mistake by Cork keeper Mark McNulty.
Derry dominated the clear-cut scoring chances in the opening period without ever troubling McNulty.
Stephen McLaughlin headed the ball home in the 17th minute but that effort was ruled out for a push on a defender.
In the 25th minute, striker Mark Farren raced through but he was denied by a magnificent last-ditch tackle by Gavin Kavanagh.
And while Farren then beat McNulty in a race for possession, his goalbound shot was blocked by the retreating Kavanagh.
In the 32nd minute McLaughlin brought the best out of McNulty, the keeper doing well to parry the shot as the home side continued to boss the ball. However, Cork were always dangerous on the break and they went so close to making the breakthrough when Daryl Horgan crashed an effort off the crossbar in the 34th minute.
But three minutes after the break Derry were rewarded for their persistence. Farren raced onto an incisive Barry Molloy pass before guiding the ball home with his right foot.
And Derry doubled their lead in the 52nd minute when McNulty appeared to misjudge a high ball, leaving McLaughlin with time and space to guide the ball into an empty net.
The introduction of three Cork substitutes in the 61st minute signalled Tommy Dunne’s intentions and while the Leesiders did look more threatening, they failed to seriously trouble Derry keeper Gerard Doherty.
Plenty then for City boss Tommy Dunne to ponder.
DERRY CITY: Doherty; Madden, Greacen, McBride, McCaffrey; McEleney (Crossan 76), Higgins, Molloy, McLaughlin (McGroary 88); Morrison (McDaid 56), Farren.
CORK CITY: McNulty; Turner, Kavanagh, Murray, Murphy; Horgan, Morrissey, Dunleavy, O’Connor (Healy 61); O’Neill (Purcell 61), Sullivan (Morrissey 61).
Referee: R Rogers (Dublin).