Ross Colton and Point scored 1:06 apart in the third period to erase a one-goal deficit and snap a three-game losing streak for the Lightning.
''We've played a lot of hockey and pucks have not been going in as easily,'' Lightning coach Jon Cooper said. ''It's games like this when you're battling back and down one with six (minutes) to go ... you just have to keep working to come out of these.''
Andrei Vasilevskiy finished with 36 saves to pick up the win.
Eric Robinson and Zach Werenski scored for Columbus, which has one win in the past six games.
Elvis Merzlikins finished with 31 saves for the Blue Jackets.
''I thought 99 percent of this hockey club played their (butts) off tonight,'' Columbus coach John Tortorella said. ''I'm frustrated for the guys because I think they've really concentrated on how we're trying to play right now. To get belief you need results and just to get nothing tonight ... it's a tough one to eat.''
Point scored the winner and his second of the game coming in on a 2-on-1 rush and as he tried to backhand a pass over to Tyler Johnson, the puck ramped off the stick of Columbus defenseman David Savard and into the net at 15:54.
''I felt like I had some jump tonight, I think our team had some jump and when we're skating that's when we're creating chances,'' Point said. ''When Columbus goes up they do a good job of shutting it down.''
Colton tied the game 66 seconds earlier with a wrist shot from the middle of the left circle.
''I had passed up on a shot like that earlier in the game when I tried to cut to the middle,'' Colton said. ''So that time I just wanted to get the puck on net and I was lucky that it went in.''
The goal answered Robinson's breakaway conversion at 10:54 that put Columbus in front for the first time in the game.
''It felt really good at the time,'' Robinson said.
Tampa Bay took the lead when Columbus was whistled for too many men on the ice while on the penalty kill to give the Lightning 62 seconds of a two-man advantage. Point cashed in with 15 seconds remaining on the 5-on-3 chance with a shot from the bottom of the left circle that powered its way through Merzlikins at 15:45.
The Blue Jackets pushed back in the second period and found the equalizer as Werenski cut across the top of the crease to swat in a rebound off his backhand for the defenseman's fifth of the season at 9:04 of the second period.
''We played good ... found a way to lose,'' Werenski said. ''It's tough right now. It's one of those things where I thought it was one of our better hockey games and we find a way to lose again. Right now we need results.''
MAC IS BACK
Tampa Bay D Ryan McDonagh returned to the lineup after missing the previous four games with an undisclosed lower-body injury, but the Lightning remain thin on defense. Erik Cernak missed his fourth consecutive game since taking a puck off the inside of his knee on March 22 in Dallas while Jan Rutta was placed on injured reserve after leaving Tuesday's game against Columbus with a lower-body injury. Tampa Bay called up D Ben Thomas from the Syracuse Crunch and assigned him to the taxi squad.
While Columbus G Joonas Korpisalo returned to the lineup after missing three games with a lower body injury, he dressed as the backup to Elvis Merzlikins, who made his fourth consecutive start, his longest stretch this season.
''These kind of games are going to help me go where I want to go, which is up,'' Merzlikins said.
Blue Jackets: At Florida Panthers on Saturday and Sunday.
Lightning: Host Detroit Red Wings on Saturday and Sunday.
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