However Highfield were giving as good as they got, and they took the lead before half-time. The Cork side took advantage of a rare Galwegians defensive lapse to crash over from a lineout move, with Donna Hughes claiming the touchdown.
This was converted by the Ireland-capped Geraldine Rea to put Highfield 7-3 up at the break.
The second half was again a closely-contested affair, with neither defence in the mood to concede much. The turning point of the match came with 15 minutes left on the clock, when Highfield centre Rea was sin-binned for a high tackle near her own 22.
'Wegians captain Emer O'Dowd passed up the opportunity to kick at goal and instead opted for a scrum. And while the initial move did not lead directly to a score, the pressure soon told on the Highfield defence.
Following a few phases of patient attacking rugby, some good handling created an overlap and Galwegians hooker Tosh Haywood seized the opportunity to dive over for the crucial try. Raftery added the conversion to put the Blues 10-7 in front.
This led to an inevitable fight-back from the Cork women who then laid siege to the Galwegians try-line. However some resolute Blues defence and discipline kept them at bay.
Then in a crucial play, a superb tackle by Raftery forced a turnover, and Lisa McDonagh fed former Ireland international Nuala Ni Chadhain who broke upfield and kicked deep into opposition territory to relieve the pressure.
'Wegians then used all their guile and experience to close out the game in the visitors' 22. The icing on the cake came when Raftery struck a final penalty between the posts with the last kick of the game, sparking wild celebrations from the Blues and their supporters.
GALWEGIANS WOMEN: Becky McPhilbin; Sarah Healy, Lisa McDonagh, Nuala Ni Chadhain, Margaret Fitzgibbon; Clare Raftery, Sorcha Ni Chadhain; Ruth O'Reilly, Tosh Haywood, Sarah Brennan, Heather Cary, Katie McDonagh, Maire Murray, Carol Staunton, Emer O'Dowd (capt).
Replacements used: Laura Feely for Murray (25 mins, blood sub), Anne O'Callaghan for Healy (60).