Dale Weise scored the game-winning goal 18:08 into overtime as the Montreal Canadiens beat Tampa Bay 5-4 in Game One of their first-round playoff series.
Montreal twice led in the third period but could not shake the Lightning in the thrilling opener.
Game Two of the best-of-seven series is on Friday.
Elsewhere, Brandon Sutter's goal with 11:42 remaining capped a rally from a two-goal deficit as the Pittsburgh Penguins beat the Columbus Blue Jackets 4-3 in the first game of their first-round Stanley Cup playoff series.
The Blue Jackets were looking for their first playoff win in the franchise's 14-year history, but lost to Pittsburgh for the sixth time this season.
The Anaheim Ducks narrowly avoided blowing a four-goal lead to hang on for a tense 4-3 victory over the Dallas Stars in the first game of their Western Conference playoff series.