The top-seeded Golden Bears were facing a must-win situation in their second and final preliminary round contest after dropping their opener 2-1 to Waterloo on Thursday.
Alberta can still advance to Sunday's gold-medal game if Saint Mary's beats the Warriors by a 1-0 or 2-1 score on Saturday. The Huskies get to play for the University Cup if they win by any other score.
"We'll worry about the various scenarios in a few hours. We get to live another day, and for now it’s all that matters," said first-year Alberta coach Ian Herbers. "I thought we had lots of energy in the early goings but, like yesterday, we couldn't buy a goal."
After outshooting Waterloo 43-13 on Thursday, the Canada West champions double Saint Mary’s 40-20 in their second outing, including 17-5 in the opening period, which ended 1-1.
"It's pretty simple. We only win 1-0 or 2-1 tomorrow and we go home," said Huskies coach Trevor Stienburg. "This is nothing new for us. We've battled and overcame adversity all year. This is just another challenge. The guys will be ready."
With Alberta leading 2-1 early in the second period, Cory Tanaka and Michael Stickland scored 29 seconds apart to give Saint Mary's a 3-2 edge.
The two quick goals signalled the end for CIS goaltender of the year Kurtis Mucha, who allowed three goals on only seven shots after being beaten twice on 13 shots on Thursday.
Johnny Lazo scored for Alberta at 7:35 of the third period to force overtime.
Mark Tipoff opened the scoring for the Huskies 15:48 into the match.
Torrie Dyck made it 1-1 with 18 seconds left before the first intermission, and Jordan Hickmott gave Alberta a 2-1 advantage at 2:13 of the second.
Host Saskatchewan met UQTR later Friday.