Derry went into an 18th minute lead when a long ball from Peter Hutton found Killan Brennan who beat Waterford keeper Holden with a low drive at the near post.
Waterfords new manager Brendan Rea saw his side draw level in the 31st minute when Mulcahy hit a first time pass that released Paul Crowley who hit a great lob over the advancing Derry keeper.
Derry regained the lead in the 42nd minute when Mark Farron ran on to a Barry Molloy pass and left the Waterford defence trailing in his wake before lifting the ball over Holden.
Waterford missed a couple of chances either side of the half and Derry made them pay for those misses by making the game safe with a third goal. Ciaren Martyn won the ball in midfield and he released Mark Farron who slotted home his second goal of the game.
WATERFORD UNITED - Holden; Andrews, Finn, Mulcahy, Doherty; Purcell, Kavanagh (Lester 83), Crowley (Grant 68), Sullivan; Banville (Waters 65), Heffernan.
DERRY CITY - Forde; Hutton, Delaney (booked 40), Higgins (McLoughlin 88), Martyn (booked 76); Beckett, Brennan, McGlynn (Cash 78), Molloy; Farron (Murphy 82), McChristal.