They also matched the best start in franchise history at 6-2-1, set in 1982-83 when the team was in Winnipeg.
"It's a measuring stick to play the best team in hockey and we went out and got the job done," Tkachuk said. "We're sick of being a below-average hockey team. We've got to make the step and why not do it this year?"
It was the fourth consecutive defeat for the two-time defending Stanley Cup champion Red Wings, who are 2-5-0 since starting the season 4-1-0.
Detroit lost four games in a row in October 1993 -- coach Scotty Bowman's first month on the job.
everyone on this team is feeling good about their game right now," said Detroit forward Brendan Shanahan, who played in his 800th NHL game.
Keith Tkchuk's sixth goal of the season helped put Detroit away. (AP)
Cummins, a rugged wing known more for his fighting ability than his scoring prowess, put Phoenix up 1-0 at 6:33 of the first period. He fought off the checking of Mathieu Dandenault and one-armed a shot past Red Wings goaltender Chris Osgood.
"It was just a play up the board and the puck came to me and I got in a foot race," Cummins said. "I outmuscled him (Dandenault) and just threw it at the net. I don't think the goalie expected it and it went in.
"I haven't scored a goal in awhile. I forgot what it felt like."
It was Cummins' first goal for the Coyotes, who obtained him from Chicago late last season, and his first since Mar. 23, 1997, when he scored against Detroit. Three of Cummins' 15 career goals have come against the Red Wings.
Tkachuk made it 2-0 with 3:12 remaining in the first period when he stepped out of the penalty box, took a pass from Corkum at the blue line and beat Osgood on a breakaway.
Nicklas Lidstrom cut Detroit's deficit to 2-1 at 6:36 of the second period on a power-play slap shot from the blue line. The shot ended a streak of five scoreless periods by Khabibulin, whose career record against Detroit is just 5-9-3.
It was the first meeting of the teams since the first round of the playoffs, which the Red Wings won in six games, and it had a playoff-type intensity.
"There was still some animosity after getting knocked out of the playoffs by them," Tkachuk said.
Phoenix's Dallas Drake suffered a mild concussion when he was elbowed in the head in the first period by Detroit's Darren McCarty, who was called for a charging penalty. Drake didn't return.
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