Fraser scored 1:19 into overtime to give Bruins a 1-0 road victory over Montreal and even the best-of-seven Eastern Conference semi-final series at two games each.
Fraser was at a restaurant in Rhode Island on Wednesday when he got the call.
"I was sitting at Chipotle eating lunch and I wondered what I was going to do for the day," said the 23-year-old rookie, who scored two goals in 14 regular season games with Boston during the regular season.
Rask made 33 saves in regulation, he did not face a single shot in overtime. The Bruins had 35 shots on Price, including three in the extra session.
"It was a hard-nosed game played by two teams well prepared," said Canadiens coach Michel Therrien.
"Both goalies were phenomenal tonight. We lost a battle in front of the net, obviously, on the winning goal, but I'm pleased with our team effort. The guys battled hard, and when you get to the overtime it could go both ways."
Montreal defenseman Josh Gorges lamented a missed chance to put Boston on the ropes, but said it was time to forget about what might have been.
"There's no sense sitting here feeling sorry for ourselves. We knew this was going to be a long series. That's a good team we're playing over there."
Game Five is in Boston on Saturday. (Editing by Peter Rutherford)