Chicago ended a three-game losing streak. Crawford had been in goal for all three setbacks after having won seven in a row.
Detroit came into the game averaging 3.3 goals per contest, third best in the NHL.
Patrick Sharp and Bryan Bickell scored during the first 4:32 of the contest to give Chicago a 2-0 lead. Patrick Eaves brought Detroit within one just 27 seconds after Bickell's goal but that was all the damage the Red Wings could do against Crawford.
Tomas Kopecky finished the scoring with a wrist shot midway through the second period and an empty-netter with 1:04 left in the third.
Sharp's goal was his 18th, moving him into a tie for third place on the NHL's scoring list.
Detroit had won three of its previous four goals. Jimmy Howard stopped 27 shots in the loss.