Aaron Greene's first-half strike gives the leaders victory in the top-two game at the Brandywell.
The striker broke clear before slotting in three minutes before the break.
It came seconds after Derry's best chance with Junior Ogedi-Uzokwe failing to connect cleanly with a David Parkhouse cross.
Parkhouse squandered a chance to equalise in the second half when he shot straight at keeper Alan Mannus.
Derry City: Cherrie, Harkin, Sloggett, Parkhouse, Ogedi-Uzokwe, Toal, McClean, Stokes, Cole, Gilchrist, B McNamee.
Subs: Gartside, McDermott, Coll, Bruna, Tweed, S McNamee, Kerr.
Shamrock Rovers: Mannus, Lopes, Grace, Watts, Finn, McEneff, S Kavanagh, Clarke, Greene, O'Brien, Byrne.
Subs: Pohls, Carr, Furlong, Coustrain, Dillon, B Kavanagh, Vojic.