Jakub Kindl in the second period and Daniel Cleary with just 39 seconds remaining of the third scored the goals as the Red Wings took a 3-1 lead over the Presidents' Trophy winners in the best-of-seven series.
The Blackhawks will try to stay alive in game five at United Center on Saturday.
Chris Kreider scored an overtime winner as the New York Rangers avoided elimination with a 4-3 victory over the Boston Bruins.
At 3-0 down in the series, the Rangers appeared to be heading out as the Bruins established a 2-0 lead in the second and then, after New York battled back to level, a 3-2 advantage in the third.
But Brian Boyle scored a power-play goal halfway through the third, then Kreider made the decisive contribution in OT.
The Los Angeles Kings edged ahead of the San Jose Sharks with a 3-0 win, which put them 3-2 up in the series.
Anze Kopitar, Slava Voynov and Jeff Carter scored for the Kings, who will look to finish off the series on Sunday in San Jose.