The Sabres ended a three-game losing streak and won their first game since defeating Ottawa on opening night.
Hasek needed to make just three saves in the first period and turned aside eight shots in the second period before allowing a power-play goal to Zdeno Ciger 3:18 into the final period.
Mike Peca scored his second goal of the season, a power-play effort, 2:20 into the first period to give the Sabres a 1-0 lead.
Joaquin Gage stopped Brad May's initial shot, but Peca pounced on the rebound and put it past the fallen goalie.
Derek Plante scored an unassisted goal at 15:15 to extend the lead to 2-0. He picked up a loose puck, took two strides over the blue line and beat Gage with a high wrist shot from the top of the left circle.
Jason Dawe scored from close in on a tight angle 43 seconds into the second period for his first goal of the season, making it 3-0. Burridge assisted.
Gage stopped 25 of 29 shots in his first start of the season. Edmonton, which lost for the fifth time in six games, has been outscored, 29-9.