Galwegians moved up to fifth in the Division One table as they ended Old Belvedere's winning start to the campaign at Crowle Park.
In atrocious conditions, the sides split four tries, but Robert O'Beirne's two successful conversions proved crucial.
An early try from lock David Nolan had the home side 7-0 ahead at half-time.
Two tries in the space of nine minutes from Dave Mongan and Leo Auva'a put the visitors ahead, but a 58th-minute penalty try was the decisive score for the Galway men.
Scorers:
Galwegians: Tries: David Nolan, Penalty try; Cons: Robert O’Beirne 2
Old Belvedere: Tries: Dave Mongan, Leo Auva'a; Con: Eamonn Fitzgerald
