The Panthers scored three times in the third period to erase a 4-1 deficit before Vatrano tipped in a rebounded shot from Jonathan Huberdeau to win it.
''We knew we had the momentum going in overtime and (Huberdeau) has a great chance before, and I would have lost some sleep if I didn't bury that second one there,'' said Vatrano, who played in his 300th NHL game. ''A great play all the way around.''
Patric Hornqvist, Ryan Lomberg, Owen Tippett and Aleksander Barkov also scored for the Panthers, who lost only once on the five-game road swing.
''It makes the trip home a lot more fun,'' said Lomberg, who scored his first NHL goal in the third-period rally. ''When you go on road trips like this, it's a chance to come together as a group and when you take four out of five it makes it that much better.''
Oliver Bjorkstrand scored two second-period goals, Patrik Laine and Max Domi also scored and Elvis Merzlikins had 27 saves for the Blue Jackets, who have lost three straight and six of eight.
''Having a 4-1 lead in the third, you can't lose those games,'' Laine said. ''That's just a fact.''
Bjorkstrand scored on a 2-on-1 rush off a nice feed from Domi at the 6-minute mark of the second period. Bjorkstrand struck again later in the second from the right circle after Riley Nash shoveled a pass out from the behind the net.
The Panthers had a miserable second period offensively, managing just four on-target shots, but Hornqvist's deflection of Forsling's shot with 4:10 left made it a one-goal game.
Laine rifled in a shot from the left circle on a power play early in the third. Domi slid in a shot from a sharp angle 80 seconds later for a 4-1 lead, but the Panthers came charging back.
Lomberg batted a rebounded puck out of the air and past Merzlikins for his first NHL goal. Tippett's goal cut the lead to 4-3, and Barkov tied the score with a wrist shot from the right circle on a power play with 5:34 left.
''It's a game you don't expect to win at that stage, but I like the resiliency, I like the excitement on the bench,'' Florida coach Joel Quenneville said. ''Everybody stuck with it. Multiple guys were contributing.''
The Panthers have picked up some momentum and are tied with with Tampa Bay for second place in the Central Division, one point behind Carolina. ''We've tested ourselves against the best in the league, and now we're right there with them, we're getting the wins we're supposed to and we know we're competing with the top teams in the league night in and night out,'' Vatrano said. ''Even some of the games we're losing, we're right in there at the end. We've got to keep this thing going.''
THE BRIGHT SIDE?
Coach John Tortorella said despite his team team blowing a big lead, the Blue Jackets are improving. ''I think our whole concept of how we're trying to play is getting better,'' he said. ''You may think I'm nuts saying it after losing a game like this, but I'm going to look at the stuff that got us to the point we were up 4-1.''
ELVIS IS BACK
Merzlikins got his first start since Feb. 20 after spending two weeks on injured reserve because of a bone bruise in his left shoulder. Joonas Korpisalo started all eight games while Merzlikins was sidelined.
Panthers: A two-game series at home against Chicago opens Saturday.
Blue Jackets: Host Dallas on Saturday and Sunday.
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