The win leaves City just three points behind league leaders Shelbourne who top the table with 25 points.
Patching converted a penalty for his third goal of the season in the 38th minute after substitute Daniel Kelly had been tripped inside the area.
That gave the Candystripes a deserved half-time lead and soon after the restart Hoban shot narrowly over.
Kelly headed straight at the keeper from Paul McMullan’s cross to the back post.
Waterford came back into the game with Rowan McDonald shooting narrowly over Brian Maher’s bar.
The impressive Hoban added the second goal when the ball fell invitingly to him and he hammered into the net from a few yards out on 74 minutes.
The hosts almost grabbed a late consolation but Padraig Amond saw his effort crash off the bar.
The result sees Derry clinch their first away win of the season and back-to-back victories for the first time in the campaign.
Ruaidhri Higgins’ side leapfrog Shamrock Rovers into second spot in the table and sit three points behind pacesetters Shelbourne.
Next up for Derry City is an away trip to Galway next Friday, May 3.
Waterford FC: Sam Sargeant; Darragh Power, Grant Horton, Rowan McDonald, Ben McCormack (Christie Pattisson 76), Padraig Amond, Connor Parsons, Maleace Asamoah (Conor Evans 63), Darragh Leahy, Robbie McCourt (Kacper Radkowski 76), Harvey Mcadam (Dean McMenamy 88).
Derry City: Brian Maher; Ronan Boyce, Ciaran Coll, Mark Connolly, Patrick Hoban, Paul McMullan (Ciaron Harkin 90), Ben Doherty (Daniel Kelly 34), Cameron McJannett, Danny Mullen (Michael Duffy 76), Adam O’Reilly.
Referee: Alan Patchell
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