Graham Cummins netted the decisive goal as Cobh Ramblers' recovery mission received three priceless points at Terryland Park.
Cummins' second minute strike was the only goal of a drab game, as Cobh were rarely troubled by the disappointing hosts.
After Galway suffered an unfortunate defeat to title chasers Bohemians at Dalymount Park on Friday evening, manager Jeff Kenna opted for the same starting XI that delivered a neat display in Phibsboro.
Cobh's recent form has been littered with narrow losses and with several regulars absent through injuries and suspensions, Stephen Henderson's team were keen to avoid another reversal.
Ramblers' cause was aided after only 90 seconds as the visitors made an ideal start when Graham Cummins finished a move that featured Alan Carey and John Kearney by slotting past Gary Rogers.
Cummins' cute strike increased the pressure on Galway, who struggled to cope with the burden during a first half in which Cobh defended with commendable conviction.
Shortly after the restart Cummins might have added a second, but Gary Rogers denied the lively Cobh attacker.
Indeed in the dying stages as Galway went with three at the back Cummins went close again, but dragged a shot wide.
Inevitably Galway had a gilt edged chance, but Mark Leech crashed over, and Cobh held on to claim the spoils.
Galway United: Rogers; Nootimer, Charles, Fitzgerald (Fenn, 83), McCulloch; O’Shea, Deegan, Russell, O'Brien; Leech, Glynn (Faherty, 60).
Cobh Ramblers: Fennelly; Carey, Murray, McCarthy, J Meade; Cambridge, Mulconry, J Kearney, Barrett, O'Neill; Cummins.
Referee: M Gough (Limerick).
