Johan Franzen and Tomas Holmstrom each tallied for the Red Wings, who had a three-game winning streak snapped. Chris Osgood bounced back from a rough start, but still got the loss in a 32-save effort.
Trailing by two to start the third, the Red Wings cut it to one 3:56 in as Pavel Datsyuk had two whacks at the puck from the low left circle, both of which Bryzgalov stopped, but Holmstrom was there to bang home the rebound.
Bryzgalov bore down from there and was able to make the stops and keep the Red Wings from evening the score with Korpikoski's empty-netter in the final minute sealing the win.
It was all Phoenix in the first period as the team scored three times to take a 3-0 lead.
The first goal came seven minutes in when Vrbata skated in on a breakaway, deked to the backhand and slid the puck past a sprawled-out Osgood for his third goal of the season.
The next came less than two minutes later when Yandle took a pass at the right circle, held the puck for several seconds then wristed a shot over the left shoulder of Osgood for a power-play goal.
Skating shorthanded, Korpikoski's wrister on the fly from the left circle sailed past Osgood with 8:04 left in the first.
Detroit got one back on the power play with under seven minutes to play in the second when a shot from the left point by Jiri Hudler was redirected into the net by Franzen to make it a 3-1 game.
The Coyotes host Tampa Bay on Saturday...Detroit hosts the Predators on Saturday...Detroit took a 2-1 win in overtime at Phoenix on October 16...Phoenix was 1-for-5 on the power play while Detroit was 1-for-6.