It was a cagey start to the game, despite Eva Noone kicking a point for Galway inside the first minute.
The Tribeswomen had to wait another eight minutes to register their second score with Hannah Noone stroking between the posts when she could have gone for goal.
The game gradually opened up and an Aimee Mackin free eventually got Armagh off the mark on 11 minutes, before Galway hit back with four successive points from play to stretch their lead.
Hannah Noone then went close to a goal as she drove forward and saw her looping strike clip the crossbar and bounce away.
Armagh were struggling to create shooting chances from open play but got another score from a free, this time from the boot of Kelly Mallon.
All-Star forward Olivia Divilly eventually got her first score with Mackin responding at the other end as her effort dropped just over the crossbar when it looked to be heading in for a goal.
Galway ended the half strongly with three scores in a row to lead by seven at the break.
They picked up where they left off after the break with Coen nailing a free after a goal chance was blocked down but Armagh responded at the other end.
Nicola Ward then had a low shot blocked with Roisin Leonard on target with the resulting two-point free and they tagged on another point to extend their advantage.
The two teams then traded scores before Galway rattled off four in a row to cruise to a big win.