Joey Anderson had given Chicago a 3-2 lead at 6:10 of the third when he scored from the left circle off an offensive-zone face-off. It was his first goal in six games since being acquired from the Toronto Maple Leafs on Feb. 27.
Dylan Larkin also scored, Alex Chiasson had two assists, and Ville Husso made 17 saves for the Red Wings (29-26-9), who were outscored 27-9 during the losing streak (0-5-1).
Detroit is six points behind the Pittsburgh Penguins for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
"I liked this game a ton," Red Wings coach Derek Lalonde said. "We've talked about not giving up on the season, and tonight was a perfect example of that. We were down 2-0, had an unbelievable second period, then got down 3-2 and still came back."
Taylor Raddysh scored twice, and Alex Stalock made 37 saves for the Blackhawks (22-37-5), who have lost five of their past six.
"Whatever we did to prepare for this game, it wasn't good enough for the NHL," Chicago coach Luke Richardson said. "I thought we were sloppy right from the start, and the only reason we were close was our goaltender."
Stalock made 12 saves in the first period, including stopping a deflection by Robby Fabbri at 4:08 before making a sprawling save with the edge of his glove on Filip Zadina at 4:11.
"That's a good team over there, even if they've been struggling for wins, and we let them regain the momentum in their building," Stalock said. "That's always going to hurt you in this league."
Raddysh gave the Blackhawks a 1-0 lead at 15:51 on a power play, scoring on a cross-crease pass by Lukas Reichel. He then made it 2-0 at 17:58 with a wrist shot from the right circle.