The win helps to move Derry above Bray but leaves Monaghan languishing at the bottom, without a home win.
After a dull first half, a defensive mix-up gifted David McDaid a chance and he didn’t fluff his lines as he slid the ball past Michael Schlingermann in the 55th minute.
Stephen McLoughlin got Derry’s second on 68 minutes as the Candystripes turned the screw.
Derry then stretched their lead on 89 minutes through Patrick McEleney.
Conor Murphy did get a consolation for Mons in injury time but Derry had the last say as Rory Patterson grabbed a fourth in the dying seconds of the added time to wrap up an easy win.
MONAGHAN UNITED: Schlingermann; McMahon, Collins (McGuinness 57), Maher (Reynor 45), Collins; Ryan, Maher, Keegan, Marks; Humphrey (Griffiths 55), Murphy.
DERRY CITY: Doherty; Madden, McCaffrey, McBride, McEleney; Higgins, McEleney, Patterson; McDaid, McLaughlin, Morrison (McGroary 75).
Referee: Derek Tomney (Dublin).