All 12 teams in the men's tournament will advance out of the round-robin but Sunday's games will determine the matchups for the first knockout phase.
Michael Grabner scored twice for Austria, bringing his tournament total to five, while Per-Age Skroder had Norway's goal.
The top finishers in each of the three groups and the team with the best second place record advance directly to the quarter-finals.
The remaining eight teams will play off with the four winners advancing.
Finland and Canada, both with 2-0 records, play later on Sunday to determine top spot in Group B while Austria (1-2) will finish third and winless Norway (0-3) fourth.