Substitute Chloe Singleton's 82nd-minute goal ensured Galway WFC advanced to the last four of the FAI Cup at Eamonn Deacy Park.
A tight and tense encounter was decided by Singleton's crisp finish late on as Stephen Lally's improving team delivered a defiant display.
The progressive DLR Waves had gone close in the 65th minute, but Galway's teenage goalkeeper Leah Hayes Coen denied replacement Katie Malone.
Fortunate to have survived that scare, Galway, prompted by Emma Starr and Meabh De Burca's industry, finished strongly.
A lively first half unfolded in the west as both teams thundered into the game.
DLR Waves defender Niamh Barnes was alert when making a brilliant challenge to thwart Rachel Kearns early on.
At the opposite end of the pitch, Carla McManus was a threat, but chances were scarce.
It still remained an interesting tussle played at a good tempo with the stakes piled high.
After the interval, a Shauna Carroll corner kick caused panic in the Galway area, but the home team survived.
Then Malone was denied by Hayes Coen, who made a brilliant stop to keep Galway on terms.
With Mayo ladies footballer Rachel Kearns making a welcome return to action for Galway WFC, Lally's charges continued to battle.
That determination was rewarded when Singleton scampered clear in the area to rattle the back of the DLR Waves net. It was enough to edge Galway into the penultimate round of the cup.
Galway WFC: Leah Hayes Coen; Therese Kinnevey, Becky Walsh, Savannah McCarthy, Shauna Brennan; Meabh De Burca, Emma Starr, Kate Slevin; Julie Ann Russell, Rachel Kearns, Lynsey McKey (Chloe Singleton, 69).
DLR Waves: Eve Badana; Aoife Brophy, Jess Gleeson, Niamh Barnes (Avril Brierley, 85), Niamh Prior; Jetta Berrill, Fiona Donnelly, Nadine Clare, Shauna Carroll (Catherine Cronin, 75); Rachel Doyle (Katie Malone, 63); Carla McManus.
Referee: Daniel Murphy.
