Nash scored on the second of four consecutive power plays in the first 12 minutes of the final period to break a 2-2 tie. His 33rd goal of the season and second of the game came at the 7:37 mark.
The Lightning had been the only NHL team he had not scored against.
Mike Lundin and Vincent Lecavalier gave Tampa Bay a 2-1 lead heading into the third period, but the Lightning were short-handed four times in the first 12 minutes and did not have a shot until 4:35 remained.
Fedor Tyutin tied it at 6:21 of the third from the high slot with a drive that hit underneath the crossbar before settling across the goal line. Nash followed with a power-play goal at 7:37.
R.J. Umberger was checked to the ice by Mattias Ohlund but still managed to backhand the puck to Nash in the low slot for a shot that trickled through traffic and into the goal.
The teams were tied at 1 after the first on goals by Lundin and Nash before Lecavalier scored on the power play at 8:06 of the second.
Lightning goalie Antero Niittymaki had 13 of his 22 saves in the final period.
Steve Mason had 16 saves for Columbus.
Lecavalier put the Lightning ahead 2-1 at 8:06 of the second, scoring his 23rd only 19 seconds into a power play. He took a feed from Martin St. Louis at the right goal line, skated in front and beat Mason with a shot off the far post.
The teams exchanged goals in the first with Lundin scoring for Tampa Bay at 16:50 with a slap shot from the left faceoff circle that went past a screened Mason for his third goal.
Nash was the recipient of Lundin's turnover 74 seconds later deep in the Lightning zone and snapped a shot over the shoulder of Niittymaki.