Stamkos, who also scored an unassisted goal in the second period, beat Carolina goaltender Cam Ward with a quick wrist shot from a sharp angle after receiving a pass from Teddy Purcell during a 4-on-3 power play.
Purcell and Tim Wallace also scored as the Lightning improved their playoff hopes with a second win in two nights, pulling to within two points of the eighth and final Eastern Conference post-season slot.
The Lightning's Mathieu Garon turned aside 25-of-28 shots.
Ward managed 19 saves.
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