Strome tapped in a backdoor pass from DeBrincat on the power play to make it 2-0 at 12:40 before beating Nedeljkovic blocker side with a wrist shot to extend the lead to 3-0 at 14:27.
Strome then got his own rebound near the crease and fed Sam Lafferty, who scored his first of the season to make it 4-0 at 19:28.
"I don't know what he ate today, but I'll bet it was something special," Kubalik said. "Everything he touched was dangerous."
The Red Wings got back into the game with three goals from their second line in the second period.
Fabbri made it 4-1 at 5:45, and Bertuzzi scored his 20th of the season 56 seconds later to make it 4-2.
"After the first period, we told our guys that we still had 40 minutes left and Chicago had just scored four goals in only 20," Blashill said. "We got back to being a good O-zone team in the second period, and you see the dividends it paid."