WATCH: All Blue Jackets vs. Lightning highlights
Saad scored the game-winning goal at 4:34 of the third period playing 4-on-4. Wennberg worked the puck out of the corner and passed it into the slot for Saad, who put a wrist shot past Bishop high on the stick side to give Columbus a 4-3 lead.
Atkinson scored a shorthanded goal at 11:13 to make it 5-3, wristing a shot past Bishop after Lightning defenseman Victor Hedman lost control of the puck in the Tampa Bay zone.
"We were quick tonight, I thought we played fast," Blue Jackets coach John Tortorella said. "I think sometimes playing fast just isn't skating. I liked all parts of our game other than the final three, four minutes of the second period. I thought we played a complete game."
Palat tied the game 3-3 at 3:37 of the third during a delayed penalty call. Kucherov controlled the puck at the point and found Palat streaking to the net for a goal off a redirection.
Anderson gave the Blue Jackets a 3-1 lead at 9:02 of the second period when he scored off the rebound of his own shot. His goal came 29 seconds after Kucherov scored his 11th of the season to get the Lightning to within 2-1.
"We could have put Ben and [Andrei] Vasilevskiy in at the same time, and I don't think it would have made a difference," Tampa Bay coach Jon Cooper said. "The goaltending had nothing to do with it. We play 82 games, chalk one up to a stinker. We got taught a lesson tonight by a team that worked way harder than us."
The Lightning made it a one-goal game again with 1:32 remaining in the second when Garrison scored his first goal of the season. Garrison's initial shot was saved by Bobrovsky, who failed to control the puck. With Ryan Callahan charging the net for a follow-up attempt, Garrison tapped in the rebound.
Wennberg scored at 3:46 of the first period to give Columbus a 1-0 lead, and Foligno scored on the power play at 8:35 of the first to make it 2-0.
