Keith beat a screened Pekka Rinne with a laser from the left point. The defenceman, 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.
The Blackhawks will face St. Louis or Minnesota in the Western Conference semifinals as they try to finish an up-and-down season with their third Stanley Cup title since 2010.
James Neal had two goals for Nashville, and Matt Cullen also scored. Rinne stopped 28 shots, but the Predators bowed out in the first round for the sixth time in eight playoff appearances.
Keith retrieved the puck just inside the blue line and waited for an opening before sending a drive through a screen past Rinne's right shoulder with 3:48 left. He had two goals and five assists in the series.
Kane capped a wild first period by firing a shot from the left circle through a screen with six seconds left, tying it at 3.
Chicago rallied after Neal scored twice in the game's first 8:09 to give Nashville a 2-0 lead, and Darling gave up three goals on 12 shots.
The goalie switch came after the Blackhawks' Sharp and Nashville's Cullen scored 39 seconds apart.
The 38-year-old Cullen beat Keith along the boards and slid the puck off the post at 11:16. Blackhawks coach Joel Quenneville then went to Crawford, who had a solid regular season but was replaced by Darling after he struggled in the first two playoff games.
Toews made it a one-goal game when Sharp's slap shot from the high slot deflected off his skate on the power play.
NOTES: The Blackhawks are 13-3 in games in which they have a chance to eliminate an opponent since the 2009 Stanley Cup playoffs. ... The Predators are 1-8 when facing elimination.