Killorn, playing in his first career Stanley Cup Playoff game, scored at 7:11 of the third period to even the score 3-3. Later in the third, he carried the puck down the left side of the ice into the Montreal zone before feathering a precise pass across the ice to Steven Stamkos, who tapped in his second goal of the game to even the score again at 4-4.
Montreal, which outshot Tampa Bay 44-25, won the game 5-4 in overtime on Dale Weise's first career playoff goal. Game 2 will be played Friday (7 p.m. ET; CBC, RDS, CNBC, FS-F) at Tampa Bay Times Forum.
Making Killorn's performance even more impressive was the fact that he came into the postseason mired in a bit of a slump, with two goals and three assists in his previous 20 games.
The 24-year-old forward, who was raised in Beaconsfield, Quebec, and attended Loyola High School in Montreal before going on to Harvard, was more inclined to reflect on the loss in the series opener than recount his third-period exploits.
"We came out too tentative, but as the game went on, we got more comfortable. But the turnovers hurt us, and our play on the blue line hurt us," Killorn said. "But we have a lot to build on."
There were eight rookies in the Lightning lineup Thursday, but Killorn, who played 38 games with Tampa Bay in his rookie season in 2012-13, wasn't looking to inexperience as an excuse.
"I don't think it was nerves; everyone here knows how to play the game," he said. "All of us have played in playoffs before, and we understand there are highs and lows. The more you can stay on an even keel, the more positive you are and the better it will turn out. With us, we know we are a lot better. We know what we're dealing with now, so I think we can go up from here."