After this defeat against Galway, Derry City must defeat Kilkenny at the Brandywell on Wednesday night to dispel any threat of relegation from the Premier Division.
Galway's top scorer Eric Lavine was absent from the travelling party and manager Don O'Riordan said after the game: "The club will issue a statement of the future of Eric Lavine. It's an internal matter and the club will deal with the issue."
Galway goalkeeper David Forde gave an inspirational display, particularly during the closing stages.
The vital goal was nodded home by long-serving central defender Billy Clery in the 28th minute after goalkeeper Russell Payne misjudged a cross.
DERRY CITY: Payne; McLaughlin, Kelly, Harkin, McCallion; Doherty, Quigley (Gallagher 59 mins), Hutton, McCready (Devlin 46 mins); Parkhouse (McCaul 59 mins), Hargan.
GALWAY UNITED: Forde; Keady, Clery, Silke, Quirke; Malee (Goldby 64 mins), Sheridan, Murphy, J Moran (O'Connor 78); Ryan and B Moran.
Referee: I Stokes (Dublin).