Regina looked headed for a shutout victory when Hannah Heisler broke a 0-0 tie at 7:21 of the third period.
But North Bay's Kaitlyn McManus sent the game to overtime in dramatic fashion, scoring with 13 seconds left in regulation.
Sabrina Picard made 22 saves for the Ice Boltz (2-0-0), the Ontario representatives at the tournament. Tatum Shand stopped 26 shots for the Rebels (1-0-1), who represent the West region.
Later Monday, the Pacific region's Edmonton Thunder improved to 2-0-0 with a 4-1 victory over the Atlantic's Metro Boston Pizza, while host Fraser Valley Phantom dropped at 5-1 decision to Quebec's LHFDQ.
Amy Boucher, with two, Taylor Hughson and Nicole Gorda scored for Edmonton, while Laura Polak replied for Metro (0-2-0).
Tracie Kikuchi stopped 20 shots for the win, with Katherine Purchase making 28 saves in defeat.
Meanwhile, Eve-Audrey Picard scored twice for LHFDQ (1-1-0), while Tammy-Lee Corbeil, Alyson Matteau and Audrey Belzile had the other goals for the Quebec squad.
Samantha Schwarz replied for Fraser Valley (0-2-0) in a game that featured 19 penalties.
Valerie Lamenta made 27 saves for the win. Laticia Castillo stopped 31 shots in defeat.