The Blackhawks won their seventh in a row and extended their lead over Pittsburgh to six points in the race for the best record in the NHL. Both teams have five games remaining.
Chicago has won the President's Trophy only once in franchise history, that honor having come in 1991.
The score was tied at 3-3 heading into the third period and Chicago took the lead when Michal Handzus scored midway through the stanza. Bobby Butler then forced overtime for the Predators with 3:34 left in regulation.
Hossa produced the winning goal with Richard Clune in the penalty box for high sticking.