The Coyotes snapped a two-game skid and moved a point in front of Anaheim into second place in the Pacific Division.
Bryzgalov has 19 saves in an eight-season career that has been split between Anaheim and Phoenix.
The Phoenix goals came 57 seconds apart in the middle period with Martin Hanzal scoring on the power play and Lee Stempniak delivering his 12th goal of the season.
The Coyotes got off just 15 shots, but two of them got past Jamie Quick. Los Angeles lost its third in a row.