Patrick Mc Eleney opened the scoring on six minutes.
Rory Patterson made it 2-0 on 59 minutes.
Michael Duffy hit the third on 71 minutes before Patterson completed his hat-trick with goals on 80 and 90 minutes respectively.
Peter Hutton was in the stands serving his suspension so Martin McCann was in charge on the line.
Derry join Shamrock Rovers and St Pats in the semi finals while Finn Harps will hope to make it tonight by overcoming Avondale in their replay in Ballybofey.
After the game, Martin Holmes spoke to Assistant Manager Martin McCann and goal scorer Patrick Mc Eleney.