Gerrick Ripley, Brody Moffatt and Rayman Bassi each had 1G 1A to lead the Wolverines while Conrad Phillips chipped in with a single.
Frazer Dodd scored twice for Swan while Nathan Carl also had a marker.
Colin Ahern made 29 saves on 32 shots in his return to the line up to get the win while Mikael Foucher stop 27 shots in the loss.
Game 3 will be played on Wednesday night back in Swan River with the puck drop at 7:30PM MB time