John Tavares scored the series winner when he took the puck from behind the Lightning net, skated in front before making a quick turnaround and unleashed a shot that went in off Tampa Bay defender Darren Raddysh's skate.
Perhaps no team began the postseason with more pressure than Toronto, a talented but long-underachieving club that needed to win a playoff series for the first time since 2004 to avoid loud calls for major organizational changes.
"Obviously it's a bit of a monkey off our back and we still got plenty of work to do but this one obviously feels really great," said Maple Leafs forward Auston Matthews.
Toronto's last postseason series win came long before the arrival of gifted goal scorer Matthews (2016), explosive winger Mitch Marner (2016) and durable captain Tavares (2018).
That core trio has endured their share of playoff heartache, most recently in 2022 when Tampa Bay beat Toronto in a decisive seventh game as the Maple Leafs lost their opening postseason series for a sixth consecutive year.
And while ousting a Lightning team that reached the Stanley Cup Final in each of the previous three seasons has brought this group to unchartered territory, it is also just the first step for a Maple Leafs team with lofty ambitions.
"It's a little bit of a relief for sure just to be able to get that done," Marner said. "But got to make sure we're ready because it just gets harder and harder."
As the best-of-seven series returned to Tampa with the Maple Leafs ahead 3-2, the visitors were desperate to close things out rather than take their chances in a do-or-die seventh game.
And for once the Maple Leafs, who had gone 0-11 in series-clinching games since they last advanced, gave their eternally optimistic fan base a reason to celebrate.
Toronto opened the scoring with about six minutes left in the second period when Matthews unleashed a slapshot from the right faceoff circle that beat Andrei Vasilevskiy.
The Lightning drew level when captain Steven Stamkos, alone in front of the net, fired home a rebound with just under 16 minutes left in regulation.
The Tavares goal less than five minutes into overtime allowed the entire Maple Leafs organization and their fan base to breathe a collective sigh of relief.
See the full match summary here.
The Maple Leafs will next face the winner of Sunday's game between the top-seeded Boston Bruins and Florida Panthers.
Playoffs roundup
In Saturday's other results, the Edmonton Oilers beat the Los Angeles Kings 5-4 to win their series four games to two.
The Oilers will next meet the West's top seed the Vegas Golden Knights in the Conference semi-finals.
Lastly, the New York Rangers defeated the New Jersey Devils 5-2 at Madison Square Garden to tie their series at three games apiece.
The Rangers and Devils will play a decider in Newark on Monday.
