Derry's Mark McChrystal in an aerial duel with Vinny Faherty
Mark Farren's second-half strike gave Derry victory in Sunday's FAI Ford Cup semi-final at Terryland Park.
Jesper Jorgensen volleyed over for Galway while Gareth McGlynn and Sammy Morrow wasted City chances in a scrappy first half.
Farren scored on 64 minutes with a clinical fininsh into the bottom corner after going clear on goal.
Double-chasing Derry, who have already won the League Cup, will meet Bohemians in the decider next month.
Farren should have doubled the lead three minutes after his goal but he failed to connect with a pinpoint cross.
Both sides squandered late chances with Vinny Faherty's poor first touch denying him a clear shot from four yards.
In the dying seconds Candystripes forward Thomas Stewart sliced wide while Galway keeper Gary Rogers made a fine double-save before the danger was cleared.
The teams meet again next Sunday in a league encounter at the Brandywell.
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