The game ended 1-1 after overtime but superb finishes from Kolbrun Gardarsdottir and April Orongan in the shootout secured the hosts the extra point.
Netminder Emma Nichols impressed once again and made 30 saves, while Ellin Rees was named as GB’s player of the game.
Netminder Emma Nichols was named player of the game as she turned away 41 of the 45 shots she faced, including 18 in the first session.
GB will face Spain, Poland and hosts Iceland in the four-team competition at the Skautahollin Laugardal ice rink.
Netminder Mali Easton will replace Kayla Poole who has had to withdraw because of injury.
Ashton comes across from his previous assistant coach role with GB Women and will be assisted by Essi Aittasalo and Darryl Morvan.