The Blackhawks, who took the Presidents' Trophy for scoring the most points in the regular season, have avoided elimination in two straight games after falling behind 3-1 in the best-of-seven series.
The series will be decided in Chicago on Wednesday with the winner advancing to the Conference final to face either the Los Angeles Kings or San Jose Sharks.
Detroit surrendered a first-period goal to Marian Hossa on Monday but got back on level terms before the intermission through Patrick Eaves, then went 2-1 up midway through the second on Joakim Andersson's wrist shot.
But the home crowd were silenced when things fell apart for the Red Wings in the third period as Chicago blitzed goaltender Jimmy Howard to seize a 4-2 lead.
Michal Handzus tied the score in the first minute of the third before Bryan Bickell and Michael Frolik gave the visitors a two-goal cushion.
Damien Brunner gave Detroit hope of a late fight back with a goal in the final minute but it was too little too late.
Chicago netminder Corey Crawford finished with 35 saves.
Detroit will be facing their second consecutive Game Seven, after their first round series against second seeds Anaheim also went the distance.
- Ice Hockey
- Sports & Recreation
- San Jose Sharks
- The Blackhawks
- Marian Hossa
- Los Angeles Kings
- Patrick Eaves