Kucherov gave Tampa Bay a 1-0 lead at 1:37 of the first period with a shot from the slot, but Bjorkstrand responded 1:22 later with a power-play goal at 2:59 to tie it 1-1.
"I thought we played well and had some chances," Bjorkstrand said. "But against a team like that, you have to be careful. They have a lot of weapons. This game is something for our group to learn from."
Stamkos put the Lightning back in front with a power-play goal at 16:47 to make it 2-1. Defenseman Victor Hedman had an assist for his 600th NHL point (134 goals, 466 assists).
"Great feeling, obviously, it happened the same way 'Stammer' got his franchise record -- me to 'Kuch,' seam pass to Stammer," Hedman said. "Perfect scenario, we've seen those a few times. It's great to get that milestone today."
Stamkos got his 100th point when he scored again at 7:29 of the second period to give Tampa Bay a 3-1 lead. He has three or more points in five straight games and 21 points during a seven-game multipoint streak (seven goals, 14 assists).
"It's been a pretty good run here in the last couple of weeks," Stamkos said. "If you would have asked me about this a couple of weeks ago, I would've settled for something less than 100.
"The power play is clicking and everything is coming together at the right time. That's more important; we want to be feeling good about ourselves going into the postseason. We're certainly trending in that direction."
Ondrej Palat scored at 14:53 of the third period with a one-timer from Kucherov for the 4-1 final.
"They shut us down pretty good in the third period," Blue Jackets defenseman Zach Werenski said. "They didn't give us very much. They're a team that knows how to win."