Keith beat a screened Pekka Rinne with a laser from the left point. The defenseman, who had the winning goal in a 4-3 double-overtime victory in the series opener, also had two assists in the clinching game.
Jonathan Toews, Patrick Kane and Patrick Sharp also scored for Chicago, and Corey Crawford stopped 13 shots after replacing Scott Darling in the first period after the rookie gave up three goals.
Chicago will face St. Louis or Minnesota in the Western Conference semifinals.
