Christoffer Ehn and Gustav Nyquist scored for the Red Wings (21-28-7), and Jonathan Bernier made 31 saves.
Detroit, which played the second game of a back-to-back (it lost 3-1 at the Buffalo Sabres on Saturday), is 3-3-0 in its past six games after going 3-9-2 in its previous 14.
Kahun gave the Blackhawks a 1-0 lead at 11:04 of the first period when his pass to DeBrincat on a 2-on-1 hit Red Wings defenseman Danny DeKeyser and bounced back to Kahun.
Strome made it 2-0 at 18:03 owhen he scored from the left side of the crease after Kahun passed it to him on a 2-on-1 as they crashed the net.
Ehn made it 2-1 at 15:00 of the second period from the left circle after Kane turned the puck over along the boards in the defensive zone.
"DeKeyser made a good play on the blue line, creating a turnover," Ehn said. "I just came in, full stride, and picked up the puck. I think the shot hit off the defender and got a lucky bounce."
Kahun made it 3-1 at 7:45 of the third period, backhanding the puck between Bernier's pads.
Nyquist made it 3-2 at 15:30, shooting the puck over Ward's glove from the slot.
"I got the puck from (Nick) Jensen and I felt I didn't have a shooting lane, so I tried to fake it first," Ehn said. "It's not a goal if (Justin Abdelkader's) not in front there. The goalie doesn't seen anything, so give (Abdelkader) credit there."
Toews scored into an empty net off a pass from Kane for the 5-2 final at 17:59 of the third. He has 14 points (seven goals, seven assists) in a seven-game point streak.