Darren Kelly in Kinnegad
Nicole Owens was the late match-winner as TG4 All-Ireland champions Dublin booked a Lidl National League Division 1 final appearance against Mayo on May 6.
Mick Bohan's Sky Blues will hope to seal a very first top-flight League title when they tackle the Westerners in what will be a repeat of last year's TG4 senior decider.
Bohan's charges never led through the 60 minutes before Owens started the move that resulted in her hitting the net in the final minute to give Dublin the advantage.
Galway hit the ground running at the start, finishing to the net inside 60 seconds.
Tracey Leonard, Caitriona Cormican and Nicola Ward did the spadework to set up Leanne Coen before a Leonard free on four minutes left it 1-1 to 0-0.
Dublin were creating and they forced two saves from Dearbhla Gower but did open through a Sinead Aherne free on eight minutes.
Leonard and Sinead Goldrick traded white flags but when Dublin did equalise on 20 minutes, their goal was as slick as Galway's first.
Aherne and Emily Flanagan carved open space on the right before Lyndsey Davey was allowed her shot.
Her attack needed assistance and Niamh McEvoy was placed to hit the net and the Leinster side were back in it.
A strong wind favoured Galway in the first half and they needed an interval cushion.
They gave the perfect response on 23 minutes when Aine McDonagh found Mairead Seoighe to her right and she found the top corner to make it 2-3 to 1-3.
Leonard and Olivia Divilly added points as Dublin went down to 14 players following an Olwen Carey yellow card - but Aherne's kick before the break left four between them.
The second half's commencement started with Dublin still favoured but as time passed, they struggled to unlock their opponents.
Galway were 2-7 to 1-5 ahead on 38 minutes with Coen and Leonard raising white flags but that was their final score.
Lauren Magee had scored the Dublin minor and they gradually reduced arrears with McEvoy, Noelle Healy and Aherne reducing the gap entering stoppage time.
Both defences were working hard and both managements brought on fresh legs. It was always going to take something special to decide it and Owens delivered when required, starting the move and interchanging passes with a couple of team mates before getting bagging the crucial goal.
Galway needed one more point to force extra time and they had a late free that tailed just wide, as Dublin prevailed.
Dublin - Niamh McEvoy 1-1, Sinead Aherne 0-3 (all frees), Nicole Owens 1-0, Noelle Healy 0-2, Sinead Goldrick 0-1, Lauren Magee 0-1.
Galway - Tracey Leonard 0-5 (four frees), Leanne Coen 1-1, Mairead Seoighe 1-0, Olivia Divilly 0-1.
Dublin: Ciara Trant; Martha Byrne, Deirdre Murphy, Leah Caffrey; Siobhan McGrath, Sinead Goldrick, Niamh Collins; Lauren Magee, Olwen Carey; Hannah O'Neill, Niamh McEvoy, Lyndsey Davey; Emily Flanagan, Noelle Healy, Sinead Aherne. Subs used: Nicole Owens for Flanagan (HT), Aoife Kane for McGrath (40 mins), Jennifer Dunne for O'Neill (42 mins), Eabha Rutledge for Davey (53 mins), Siobhan Killeen for Magee (57 mins).
Galway: Dearbhla Gower; Fabienne Cooney, Sarah Lynch, Sinead Burke; Charlotte Cooney, Nicola Ward, Caitriona Cormican; Lisa Gannon, Olivia Divilly; Aine McDonagh, Tracey Leonard, Ailbhe Davoren; Mairead Seoighe, Sarah Conneally, Leanne Coen. Subs used: Roisin Leonard for Conneally (41 mins), Deirdre Brennan for Coen (46 mins), Emma Reaney for Seoighe (54 mins).
Referee: Seamus Mulvihill (Kerry).