Columbus was trailing 2-1 in the third period when Nathan Horton notched the equalizer on a power play early the final period.
The Blue Jackets were handed another man-advantage with 3:28 left when Tampa Bay's Tyler Johnson was whistled for holding, and Johnson made the Lightning pay with wrist shot from the high slot that got past Anders Lindback.
Ryan Johansen also scored and Sergei Bobrovsky stopped 26 shots as Columbus claimed a fourth straight win.
Victor Hedman and Alex Killorn each scored for the Bolts.
Lindback finished with 25 stops.