In the first period, the Blue Jackets outshot the Lightning 20-6, won 17 of 20 face-offs, and killed a penalty against the top-ranked power play in the NHL (30.3 percent), but they trailed 2-0 on two goals by Kucherov.
"We had a really good first period. We definitely dominated that period," Columbus forward Kole Sherwood said. "They got two lucky bounces and capitalized on them."
Kucherov scored with a backhand shot to the right post to make it 1-0 at 11:18 off a 2-on-1 pass from Yanni Gourde after a Blue Jackets turnover.
On his second goal, he stole the puck from Nick Foligno in the neutral zone and scored unassisted to give Tampa Bay a 2-0 lead at 14:24.
"I'm frustrated for the team," Blue Jackets coach John Tortorella said. "Our first period was probably our best period of hockey we've played all year long. I'm not crazy about Nick's turnover. Again, you just can't lose your patience in a game like that.
"You're down 2-0 after the way we played, you still have to stick with it."