The Stars, who began the night two points out of a playoff position, put together a rare scoring outburst to capture their second in a row.
Marian Hossa produced a second-period goal for the Blackhawks, who had a four-game winning streak snapped.
Richard Bachman made 27 saves to get the win. He had not appeared in any of the Stars' previous 10 games.
Crawford allowed the three goals on 23 shots.
Chicago had won 21 of its 31 home games prior to Thursday.
NBC reportedly holds celebs hostage to Jimmy Fallon's show
Ray Liotta sues skin care company over use of likeness