Zibanejad gave the Rangers a 1-0 lead at 12:45 of the first period with a one-timer from the high slot.
"I thought we did a lot of good things throughout the game," Zibanejad said. "You lose in a shootout, and we're obviously not happy with just one point. We'd rather get the win. But [our] overall play was better. We just have to make sure we come away with two points next time."
Brandon Hagel thought he tied the game for the Lightning at 4:49 of the second period, but video review determined Hagel used his hand to grab and propel the puck over the goal line.
"He came back to the bench like a little kid as if that was going to get by," Cooper said. "But no, in the era of [high-definition] cameras, that's not going to work."
But Point tied it 1-1 at 5:32 of the third period when his shot from the low slot deflected off Shesterkin's blocker.
Lightning forward Steven Stamkos started the game on a line with Anthony Cirelli and Killorn but played with Point and Nikita Kucherov in the third. The three generated the tying goal.
Stamkos hasn't scored in six straight games and remains three goals shy of 500 in his NHL career.
"[They're] two of the best players in the League, so anytime you get a chance you want to make the most of the opportunity," Stamkos said. "It was nice to get that goal."