Andrei Vasilevskiy stopped 19 shots for his league-leading 28th victory of the season.
The Lightning moved to within a point of idle Florida for second place in the Central Division. Tampa Bay has played one less game than the Panthers.
Hedman, who added an assist earlier in the game, took a pass from Point in the slot and wristed home a shot past Merzlikins for his second overtime goal in a week.
Palat opened the scoring at 11:50, finishing off a pass by Point from below the goal line for his 14th of the season.
Columbus took the lead late in the first period with a pair of goals in a 2-minute, 13-second span.
Grigorenko buried a shot from the slot to finish off a pass from Vladislav Gavrikov at 16:16. Robinson scored his first on a wraparound with 31 seconds left to carry a 2-1 lead into the first intermission.
The Lightning pulled even 6:09 into the second period with Joseph finishing a 2-on-1 break by tapping in a pass from Point for his 12th of the season.
The Blue Jackets regained the lead in the opening minute of the third period when a shot by Max Domi was blocked by Erik Cernak, but the puck bounced right to Robinson, who pounced on it and found the far side of the net at 55 seconds.
Tampa Bay tied the game again on the power play with Barre-Boulet snapping a one-time wrist shot from the left circle off a pass from Palat. It was the first NHL goal for Barre-Boulet, the 2019 American Hockey League rookie of the year.
After the goal, Korpisalo left the game with a lower body injury and was replaced by Merzlikins.
RINGS THE THING
The Lightning players and staff received their 2020 Stanley Cup championship rings in a private ceremony held outside at the house of team owners Jeff and Penny Vinik on Friday. The ring is made of 14-karat white gold and 557 custom cut diamonds and 81 custom cut blue sapphires for a total weight of 25 carats, the largest ring in total weight created by Jostens.
“With the season still going on, that was a nice little break for us to look back at what we accomplished,” defenseman Victor Hedman said. “To get that ring presented to us by our owner, the generosity is out of this world. We’re proud of what we did and that’s another sign of what we accomplished and that’s going to stay with us forever.”
KEEPING THINGS LOOSE
With Columbus officially eliminated from playoff contention, ending a franchise-best four consecutive seasons with a playoff berth, and the Blue Jackets riding an eight-game winless streak entering Sunday, head coach John Tortorella wants to take away some of the tension and frustration that has been building up in the locker room.
“I want the players to try to enjoy some of the time that is left here, so we are trying to act accordingly here,” Tortorella said. “My shift in mind-set has gone that way. They don’t deserve to be grinded. As much as the year that we’ve had has been a very bad year, I am not going to double it up and grind them through this here.”
Columbus: Host Detroit Red Wings on Tuesday.
Tampa Bay: At Chicago Blackhawks on Tuesday.