Good question, not sure? That was straight fire, man. I think 4 consecutive could be a record.
This is all I could find...
Most goals, one playoff game: Newsy Lalonde (March 1, 1919), Maurice Richard (March 23, 1944), Darryl Sittler (April 22, 1976), Reggie Leach (May 6, 1976), and Mario Lemieux (April 25, 1989), 5