Eager scored twice, and Andrew Ladd had a goal and three assists for a career-high four points in Chicago's 7-1 victory.
Jonathan Toews and Dave Bolland each had a goal and an assist, and Patrick Sharp and Dustin Byfuglien also connected. The Blackhawks scored their season-high seven goals in an 11-shot span against Ilya Bryzgalov.
Eager scored twice in a game for the second time in his career to match a personal high. Best known for his physical play, he also fought the Coyotes' David Hale midway through the second period when Chicago had a 7-0 lead.
"The guys really came to play tonight," Eager said "Score two, beat a guy up? If could do that every night I would. It's a nice feeling when everyone plays well and you help contribute."
Chicago's Cristobal Huet, making his fifth straight start with Nikolai Khabibulin sidelined by a groin injury, stopped 20 shots, allowing only Enver Lisin's goal on a breakaway in the final minute of the second period. Coming off a 5-4 shootout loss in Detroit on Saturday night, Chicago improved to 8-1-4 at home.
"I thought we played pretty well last night," Ladd said. "We wanted to come up with the same effort tonight. We figured we'd come up with a better result."
The Blackhawks were in charge throughout the contest.
"We got outplayed, outscored and outhit," Phoenix coach Wayne Gretzky said. "They took it to us pretty well."
Bryzgalov seemed as skaky as the team in front of him. He finished with 21 saves in the Coyotes' second straight loss.
During the game, team officials said Phoenix backup goalie Mikael Tellqvist was available, but not on the bench.
Following the contest, the team announced that Tellqvist had a lower-body injury. Gretzky confirmed that he didn't want to use him.
"He had a minor injury and it was one of those things where we really couldn't take a chance of him getting hurt more," Gretzky said. "We made the decision today we were going to go with Bryzgalov. It's a simple as that."
Chicago took a 4-0 lead in the first period.
Bolland opened the scoring with 8:22 left on a hard, low shot from the right circle. Toews made it 2-0 29 seconds later. Following a turnover by the Coyotes at the blue line, Toews completed a give-and-go with Martin Havlat.
Byfuglien popped in a rebound from the crease with 2:46 left, and Sharp one-timed in a power-play goal 1:18 later. Eager scored twice and Havlat once in a 2:55 span early in the second to stretch Chicago's lead to 7-0.
Versteeg received an instigator, fighting major and two game misconduct penalties. The 19-year-old Turris was assessed only a fighting major.
Gretzky was fuming on the bench as the game ended, but calm after the contest.
"What happened in the last 5 seconds, I don't like to see an 18-year-old kid [Turris] get grabbed out of a pile in a 7-1 hockey game and take a beating like that," Gretzky said. "I don't think there's any room for that.
"I've never seen anything like that. In a 7-1 hockey game, to me it doesn't make a lot of sense."
The Blackhawks' four goals in the first period matched a season high. ... Khabibulin could return within a week. ... Blackhawks RW Adam Burish sat out his sixth game because of a foot injury ... Phoenix C Olli Jokinen missed his sixth game on IR with a shoulder injury. ... Coyotes D Ken Klee was a healthy scratch. ... The crowd of 21,217 was the Blackhawks' 13th straight sellout this season.