Dane Dobbie and Shawn Evans each had two goals and two assists for the Roughnecks (8-5), who outscored Minnesota 6-2 in the fourth quarter after being tied through 45 minutes.
Curtis Dickson scored once and set up three more for Calgary and Dan MacRae, Geoff Snider, Tor Reinholdt, Karsen Leung and Matthew Dinsdale.
Shayne Jackson had three goals for the Swarm (3-10), Jordan MacIntosh and Josh Gillam each had a pair of goals, Callum Crawford scored once and set up five others while David Earl, Kiel Matisz and Scott Jones added single goals.
Mike Poulin made 40 saves for the Roughnecks. Tyler Carlson gave up 13 goals on 48 shots in 43 minutes of action for Minnesota while Zach Higgins stopped 6-of-8 shots.