Miles Thompson also scored a hat trick for Minnesota (1-1), which had nine fourth-quarter goals. Andrew Suitor and Shayne Jackson each struck twice with Jordan MacIntosh, Ethan O'Connor, Nick Cotter and Corbyn Tao also chipping in.
Chris Corbeil, Robert Church, Mark Matthews and Ben McIntosh all had two goals for the Rush (0-2). Jarrett Davis and Zack Greer rounded out the attack.
Brodie MacDonald started in net for the Swarm, stopping 21-of-30 shots in 32:22. Zach Higgins closed out the game and made 14 saves in 27:38.
Aaron Bold turned away 40 shots for Edmonton in the loss.
Minnesota converted once on five power plays while the Rush scored three goals on six chances.