The Blackhawks are 3-0 under new coach Denis Savard, who replaced the fired Trent Yawney on Monday. Chicago is also perfect in three games against Nashville this season.
Hamilton provided the difference when he skated in low in the slot and one-timed a pass from Patrick Sharp to the right of Nashville goalie Chris Mason 59 seconds into the extra session.
Scott Hartnell and Kimmo Timomen had a goal and assist each, and Shea Weber also scored for the Predators.
Tony Salmelainen had the other Blackhawks goal.