Marc Staal started the winning sequence with a long slap shot that was stopped by Corey Crawford, who also got in front of Hagelin's first rebound attempt. But Hagelin stayed with the play and flipped the puck into the open right side with 5:57 left.
It was Hagelin's fourth winning goal of the season, tops on the team. He also is tied for the team lead with 11 goals overall.
Jonathan Toews and Brandon Bollig scored in the second period for Chicago, which had recorded at least one point in a season-high 10 games. It was the Blackhawks' first home regulation loss since a 4-3 setback against Dallas on Dec. 3.