Derry moved second and level on points with Premier Division leaders Shamrock Rovers after this comfortable win at Terryland Park.
Eamon Zayed put the Candystripes ahead just before the break and James McClean made it 2-0 within 60 seconds of the restart.
Bobby Ryan pulled one back for Galway on 50 minutes before McClean completed his double.
Gareth McGlynn sealed City's victory with a 64th minute strike.
Derry started Friday evening in third but Sligo Rovers were held to a 1-1 draw at Dundalk while Shamrock Rovers needed an injury-time equaliser to draw 1-1 away to Bohemians.
Only goal difference separates Shamrock Rovers, Derry and Sligo with all three on 14 points.