The 'Candy Stripers,' who remain on top of the Premier Division table three points clear of Cork City, entered the break on level terms despite their overall domination.
However, deadlock was deservedly broken in the 50th minute when Gareth McGlynn's angled shot found the net, possibly helped home off the foot of Brian Shelley.
Derry ended the game as a contest when Mark Farren increased his goal tally for the season to 17 strikes having netted from the penalty spot.
Referee Hugh Whoriskey adjudged Ciaran Martyn to have been fouled following a corner kick.
Derry struck the post on two occasions with McGlynn clipping a shot from 18 yards off the crossbar in the dying stages.
Derry City: Forde; McCallion, Hutton, Delaney, Hargan; McGlynn, Martyn (Murphy, 86 mins.), Deery, McCourt; Beckett (O'Flynn, 77 mins.), Farren.
Shamrock Rovers: Murphy; Shelley, Foley, McDonnell, Doyle; McDonagh, Tracey (O'Halloran, 86 mins.), Rutherford; Quigley (Daniel, 61 mins.), Sheridan (Roche, 51 mins.), Molloy.