The Scottish team of Aileen Neilson, Rob McPherson, Gregor Ewan and Hugh Nibloe trailed 5-4 going into the last two ends before scoring three and two to claim a 9-5 victory.
Norway took gold with an 8-3 victory over Russia in the final.
The eventual champions beat Scotland 7-3 in Saturday's earlier semi-final.
Scotland won bronze after coming from behind to beat China at the World Wheelchair Curling Championship in South Korea.