The Blackhawks wrapped up a top-three seed in the playoffs with the victory over the Red Wings combined with a loss by St. Louis earlier in the evening at Columbus.
Chicago's Jonathan Toews scored with 2:57 left in the third period to force overtime and the Blackhawks outlasted Detroit in the marathon shootout.
Chicago won its fourth in a row.
The lone point claimed by the Red Wings ensured Detroit would remain in the No. 8 spot in the Western Conference standings. Phoenix, Dallas and Columbus are all putting heat on the Red Wings in the fight for the final post-season berth.