The score was tied 2-2 midway through the third when St. Louis recorded his 18th goal of the season on a power play.
Then with the Jets pressing for the equalizer in the late stages, he iced the victory with another into an empty net as the Lightning took a third win in four games.
Valtteri Filppula and Ondrej Palat also scored for Tampa Bay.
Alex Killorn and Teddy Purcell each provided two assists and Anders Lindback stopped 12-of-14 shots en route to the win.
Dustin Byfuglien registered a goal and an assist for the Jets, who dropped a fourth in a row.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut