"We thought we'd done a pretty good job. A 4-2 lead with a couple minutes left," Red Wings' coach Mike Babcock said. "Anyway you look at it it's a tough loss for us. We were in a situation for us to get two points and them to get none. Then they end up with two and we get one and it doesn't help build any confidence either."
Jovanovski's goal came during a goal-mouth scramble with 22 seconds left to tie it, after Yandle's 6-on-4 power-play goal with 1:30 left.
Lidstrom scored a tiebreaking goal with 8:38 to play, and added another on the power play with 4:38 left.
"We have to find a way out of this. Playing a lot better in our own zone and bearing down when we have to," Lidstrom said. "It's not fun. It's disappointing when you're giving points away the way we have been. We know we need the points right now."
Eaves tied it at 2 just 11 seconds after Phoenix took a 2-1 lead in the second period.
Yandle's first goal had put the Coyotes up by one with 7:53 left in the middle period after Upshall's power-play goal about a minute and a half earlier.
Datsyuk opened the scoring 7:58 into the game, beating Bryzgalov for his 12th goal.
Detroit D Niklas Kronwall returned after missing 30 games with a knee injury. ... Phoenix LW Daniel Winnik missed his third game with an upper body injury. ... Coyotes' D Adrian Aucoin was hit in the face with an attempted clearing pass by the Red Wings' Darren Helm halfway through the second period.