"We're only just past the 20-game mark," Coyotes coach Dave Tippett said. "I'll get excited when I feel we're good enough to do something. Give all the credit in the world to these guys for how hard they're working, but it's early."
Phoenix earned the victory despite the absence of defensemen Ed Jovanovski and Adrian Aucoin. Aucoin missed his second game because of a lower-body injury, and Jovanovski was sidelined by the flu.
Bryzgalov was rarely tested en route to his first shutout since March 13 at Carolina. He faced only four shots in the first period, and Edmonton generated few scoring chances throughout the game.
The Oilers, coming off a win in Anaheim, have not won consecutive games since the first two games of the season.
"Some guys want it to be easy, but this is the best league in the world. It's never going to be easy," Oilers center Sam Gagner said. "We think after one (win) that it's going to be easy and we forget how hard it was to get that win."
Edmonton coach Tom Renney was succinct in expressing his frustration.
"It's a joke," he said. "An absolute travesty."
Hanzal gave Phoenix a 1-0 lead 48 seconds in. He scored into the open right side of the net when goalie Devan Dubnyk overplayed Ray Whitney at the top left corner of the crease. Dubnyk left the net to prevent Whitney from shooting, but Whitney passed the puck to Hanzal, who was alone on the right doorstep.
"When you score early in the game it makes it much easier to play the game," Hanzal said.
Wolski made it 2-0 two minutes into the second period. He gained control of the puck along the right wing boards and skated toward the crease before beating Dubnyk with a quick wrist shot.
Stempniak tucked a rebound of his own shot just inside the left post at 17:07 to put the Coyotes ahead 3-0.
Hanzal netted his second with 6:15 left in the game, taking a long outlet pass from Derek Morris just outside the Oilers zone, skating to the right circle and wristing a shot over Dubnyk's right shoulder.
Stempniak capped the scoring with 51 seconds remaining.
"I think we have a good roll now and we've got to keep it rolling," Hanzal said.
NOTES: The Coyotes placed C Kyle Turris on the injured list, retroactive to Nov. 19. He is week-to-week with an undisclosed upper body injury sustained in Phoenix's last game against the Oilers in Edmonton. Coyotes RW Scottie Upshall played in his 300th NHL game. Dubnyk lost in regulation for the first time in five starts (1-1-3) since taking over for the injured Nikolai Khabibulin.