Khudobin, who was named the NHL's first star of the month for January, improved to 13-5-0 on the season as the Hurricanes won for the sixth time in eight games.
Riley Nash, Alexander Semin, Brett Bellemore, Andrej Sekera and Jiri Tlusty each scored for Carolina.
Nick Bjugstad netted the Panthers' only goal.
Tim Thomas started in net but was yanked in the second period after yielding four goals on 14 shots.
Scott Clemmensen relieved and turned aside 16-of-17 shots the rest of the way.
Notable deaths of 2014 [PHOTOS]
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