The Islanders had a 3-0 lead as the final frame began but the Panthers got scores from T.J. Brennan, Marcel Goc and Mike Santorelli within a 1-minute, 43-second span to tie it up.
New York then regained the lead when Cizikas got a pass from Colin McDonald from behind the net and one-timed a shot past Scott Clemmensen with 7:05 to go.
Evgeni Nabokov turned aside 27 shots to earn the win.
Santorelli added an assist and Clemmensen finished with 21 saves for the Panthers.
Notable deaths of 2014 [PHOTOS]