The New York Islanders had a hand in that, pulling out a 2-1 victory on Jordan Eberle's goal 12:30 into the second overtime in Game 5 of the Eastern Conference Final at Rogers Place in Edmonton on Tuesday.
So instead of advancing to the Stanley Cup Final for the first time since 2015 to face the Dallas Stars, the Lightning will have to try again against the Islanders in Game 6 of the best-of-7 series in Edmonton, the hub city for the conference finals and Cup Final, on Thursday (8 p.m. ET; NBCSN, CBC, SN, TVAS).
"That's what happens in this game," Tampa Bay coach Jon Cooper said. "We had opportunities to put the game away, and either it was a bounce here or a save here or a blocked shot here. But if you look at the game as a whole, if we keep doing that, I'm pretty confident in our group."
The Lightning have reason to feel confident. Since the NHL adopted the conference format for the 1981-82 season, teams with a 3-1 lead in the conference finals are 35-1 (97.2 percent), including the Stars' five-game win against the Vegas Golden Knights in the Western Conference Final this season.
This Game 5 had a familiar feel for Tampa Bay up until Eberle's goal. The Lightning ended each of their first two series in the Stanley Cup Playoffs with an overtime win in Game 5 and were a combined 4-0 in overtime in those two series.
Tampa Bay eliminated the Columbus Blue Jackets with a 5-4 overtime win in Game 5 in the first round and went to a second overtime before knocking out the Boston Bruins with a 3-2 victory in Game 5 in the second round.
The Lightning had the Islanders on their heels for much of the night, outshooting them 37-24. They had a golden opportunity to win the game after Islanders forward Anthony Beauvillier received a double minor for high-sticking defenseman Mikhail Sergachev with 1:23 left in the third period.
But the Lightning managed two shots on goal during the four-minute power play, which carried over to 2:37 of overtime.
Tampa Bay continued to carry play and limited New York to eight shots on goal in 32:30 of overtime. But when the Islanders got their best chance, Eberle was able to finish it to extend the series.
"Both teams played well, both goalies (Andrei Vasilevskiy for Tampa Bay and Semyon Varlamov for New York) played well, and it came down to one play," said Lightning defenseman Victor Hedman, who scored at 4:00 of the second period to tie the game 1-1. "It's tough for us, obviously, but this is hockey, and it's how you respond to this that's going to define you as a team. I'm not worried about how our group is going to respond to this. We missed an opportunity tonight, but we have a new one here in a couple of days."