Briege Corkerry with the goal for the Rebels while Niamh McGrath scored 8 points for the Connacht side.
Cork manager Paudie Murray says his team kept their composure throughout most of the game while Galway manager Tony Ward admited his team didn't play well.
Earlier in the day Laois beat Roscommon in the Premier Junior final while Waterford overcame Kildare in the intermediate decider.
