Kotkaniemi, who missed the past eight games with a concussion, scored at 2:08 of the first period to give the Canadiens a 1-0 lead.
Max Domi scored at 10:00 to make it 2-0 and extend his goal streak to four games. Play continued for 1:02 before the Situation Room contacted the off-ice officials to inform them Domi's shot crossed the goal line and have them sound the in-arena horn.
"I thought we had a good start, [17-0] on shots, we had a 2-0 lead," Canadiens forward Phillip Danault said. "We should've played better defensively. We didn't play like we've played the last couple of games."
Killorn made it 2-1 when he scored with 59 seconds left in the first. Stamkos had an assist for his 799th point.
Stamkos reached the milestone when he scored to tie the game 2-2 at 1:34 of the second.
"Another one of those things you are just fortunate enough to be in the League as long as I have, played with some great players," said Stamkos, who has 407 goals and 393 assists in 779 NHL games. "Hopefully a lot more to come, but it's again something to probably look back on when you are done, but nice to get it in a win tonight."
Mitchell Stephens scored his first NHL goal at 4:56 to give the Lightning a 3-2 lead.
"A pretty cool feeling just to get my first, and it's a big win for our team too," Stephens said. "That's two really big points for us."