After Drew Stafford was whistled for hooking less than a minute into the extra session, Stamkos beat Matt Hackett with a power-play laser glove side.
Stamkos finished with two goals and an assist while Ryan Callahan and Alex Killorn finished with a goal apiece for the Lightning, winners in seven of their last nine games. Ben Bishop allowed two goals on 28 shots in the win.
Cody Hodgson and Matt D'Agostini had one goal apiece and Cory Conacher was awarded a goal after Stamkos put one in his own net in the third period.
2014: The Year in Music [PHOTOS]