Chicago won its fourth straight and snapped a seven-game losing streak against Detroit that dated to March 2006.
By earning a point for reaching overtime, the Red Wings clinched their sixth straight Central Division title. Detroit needs one more point to secure its third consecutive Western Conference title.
Pavel Datsyuk scored in the shootout for Detroit.
Chicago's Nikolai Khabibulin made a season-high 56 saves, and Nikita Alexeev and Bryan Bickell - making his NHL debut - scored in regulation. The Blackhawks' winning streak is their longest of the season and follows a six-game losing skid.
Kyle Calder was credited with a power-play goal for Detroit at 9:36 of the third to tie it at 2 and set up overtime. However, it appeared that Robert Lang also might have jammed the loose puck past Khabibulin.
Tomas Holmstrom also scored in regulation for Detroit, which came back from a 2-0 deficit. Chris Osgood made 19 saves.
Red Wings forward Todd Bertuzzi suffered a sprained neck in the first period and didn't return.
The game was the opener of a home-and-home series between the two teams. The Red Wings host Chicago in their season finale Saturday afternoon. The Blackhawks close their season at Dallas on Sunday.
Alexeev opened the scoring 5:03 into the first. After taking a cross-ice pass from Denis Arkhipov, he beat Osgood high on the stick side with a shot from the left circle.
Bickell made it 2-0 with a deflection from the edge of the crease at 3:04 of the second. As he was pulled to the ice by Detroit's Chris Chelios, Bickell redirected Jonas Nordqvist's shot from right wing.
Both Bickell and Nordqvist were recalled from the Norfolk of the AHL earlier in the day.
Holmstrom cut it to 2-1 with 40 seconds left in the second period. Left uncovered just off the right edge of the crease, Holmstrom banged a rebound of Johan Franzen's shot between Khabibulin's pads.
Calder was credited with jamming a loose puck under Khabibulin's pads at 9:36 of the third for a power-play goal that tied it 2-2 following a video review.
Detroit outshot Chicago 5-2 in the scoreless overtime.
Notes: Detroit D Nicklas Lidstrom sat out with a sore back. ... Red Wings D Niklas Kronwall missed his third game with a fractured sacrum and is out for the season. ... Detroit LW Henrik Zetterberg missed his 18th game with a lower back injury, but has resumed skating. ... Chicago LW and leading scorer Martin Havlat is out for the season after suffering a shoulder injury Tuesday in Nashville. ... Blackhawks C Mikael Holmqvist also is out for the season with a shoulder injury suffered in Nashville. ...Chicago D Adrian Aucoin missed Thursday's game with a pulled groin.