Hossa, who sat out the previous game with an upper-body injury, played nearly 18 minutes and scored the first goal in the Blackhawks' third win in their last four games.
Crawford's Phoenix counterpart, Jason LaBarbera had a much busier night. He faced 35 shots and allowed five goals.
After Hossa gave Chicago a 1-0 lead in the first period, the two teams traded goals in the second until 8:36 when Mayers tipped the puck in to make it 3-2.
Bolland made it 4-2 at 2:27 of the third period when he stole the puck at the Phoenix blue line and scored on a short-handed unassisted slap shot.