Kucherov sent a fake-shot pass to Point in the slot on the power play to tie it 3-3 at 16:26.
Tampa Bay went 3-for-4 with the man-advantage.
"That was a big part of our game tonight, to get those power play chances and bury them," Stamkos said. "Some games, the 5-on-5 play is not where it needs to be, and you need to rely on special teams. Sometimes it's the PK, sometimes it's the PP, and tonight was a combination of both, really."
Cozens gave Buffalo a 4-3 lead when he took a no-look, behind-the-back pass from Rasmus Dahlin and scored top corner short side from the right circle at 9:37 of the third.
Jeff Skinner spun around and scored from below the right circle at 14:19 to make it 5-3.
"They're a team that knows how to win," Cozens said. "So, they're confident that they can turn it on like that in the last few minutes and score at any time. That's something we need to know, and we need to just keep pushing and not let them get those chances, because they obviously know how to win games."