Patrick Kane had two assists for the Blackhawks, who have a 40-23-7 record all-time against the Blue Jackets. Crawford, who won for the fourth time this season, was solid all night but particularly when the Blackhawks were a man down.
Steve Mason held his own with 21 saves for the Blue Jackets, who lost their third in a row.
A goal by Derick Brassard was waved off in the second period when the officials ruled Nick Foligno interfered with Crawford. That decision caused a sellout crowd of 18,381 to boo throughout the game.
Mark Letestu gave Columbus a 1-0 lead and Artem Anisimov scored late to make it interesting for the Blue Jackets, who have been outscored 12-3 in their losing skid.