To compound matters, defenseman Zach Werenski was called for slashing Steven Stamkos at the 20:00 mark of the second and the Lightning took advantage when Point added a power-play goal at 1:40 of the third to make it 5-2.
"That's the hard part right there," captain Nick Foligno said. "You battle back in the game, then an unlucky bounce, whatever you want to call it at the end. It just seemed after that we shoot ourselves in the foot with penalty after penalty and then you allow a team to take over."
Tampa Bay, which was 0 for 8 on the power play in its first two games, scored four goals in seven tries, including Alex Killorn at 7:12 of the third to go up 6-2 and J.T. Miller with a second left in the game. Columbus was 0 for 5.
In between those two goals, Nikita Kucherov scored at 13:02 of the third on Sergei Bobrovsky, who made 23 saves but allowed the most goals in his NHL career.
Andrei Vasilevskiy made 30 saves for the Lightning (2-1-0).
Victor Hedman, Cedric Paquette and Yanni Gourde gave the Lightning a 3-0 lead in the first although the Blue Jackets almost struck first.
Cam Atkinson hit the post in the opening 30 seconds and the Lightning turned it around with Hedman gliding through the slot to put in his own rebound at the 1:00 mark.
Then, during a Blue Jackets power play, Lightning defenseman Anton Stralman turned his back in front of the open net to block Foligno's shot. The Lightning countered and caught a break when Gourde tripped Pierre-Luc Dubois along the right wall without a call being made.
Gourde fed Paquette for the 2-0 lead at 11:17 just after the penalty expired and Gourde added a power-play goal at 18:37 for the three-goal advantage.
The period was reminiscent of the second period Thursday at Florida when the Panthers struck for three goals.
"It's bad hockey on our part," forward Oliver Bjorkstrand said. "Some games when you have bad periods, the key is to come back strong and make them pay for it."