Tuomo Ruutu added two goals, rookie Jonathan Toews had a goal and two assists, and NHL rookie scoring leader Patrick Kane also had two assists. Nikolai Khabibulin stopped 28 shots, allowing only Peter Mueller's breakaway goal with 7:57 left.
Byfuglien, playing his 47th NHL game, matched the Chicago record for goals in a game by a defenseman set in 1977 by Dick Redmond and matched by Doug Wilson in 1991.
Byfuglien entered the game with three goals and an assist in 12 games this season.
Phoenix goalie Ilya Bryzgalov was pulled at 10:30 of the first period after allowing five goals
- capped by Byfuglien's natural hat trick - on seven shots. Mikael Tellqvist replaced him and allowed a goal on 20 shots.
Bryzgalov, claimed off waivers from Anaheim on Nov. 17, made his sixth straight start since joining the Coyotes. In his first five games with Phoenix, he was 4-1-0 with a 1.58 goals-against average, and had allowed eight goals on 137 shots.
The Blackhawks scored on their first three shots and five times in the first period to take control early.
Ruutu opened the scoring just 1:15 in when his shot from right wing glanced in off Bryzgalov's left arm.
Toews made it 2-0 at 3:57. After Brent Sopel's centering pass to Patrick Sharp bounded back to the right circle, Toews fired in a shot with Bryzgalov out of position.
Byfuglien's first goal, made it 3-0 at 5:01. He scored from the slot after taking a centering pass from Sergei Samsonov.