Nikita Kucherov had a goal and two assists, and Andrei Vasilevskiy made 31 saves for the Lightning, who are the No. 3 seed from the Atlantic Division.
Tampa Bay, which lost 5-0 in Game 1, is 15-0 in the postseason following a loss since the beginning of the 2020 Stanley Cup Playoffs.
"I don't know how far teams go when their big guys aren't going," Lightning coach Jon Cooper said. "You need them especially at times when your back is against the wall. I can't say our back was against the wall, it was one game, but we needed them tonight and they stepped up, and it started with our goaltender. He was outstanding."
Mitch Marner had a goal and an assist, Auston Matthews had two assists, and Jack Campbell made 29 saves for the Maple Leafs, who are the No. 2 seed from the Atlantic.
"I thought they played better," Toronto coach Sheldon Keefe said. "That's really the team that we prepared for. Obviously, the difference in the game was special teams. At 5-on-5 it was a pretty even hockey game. Their power play was better. We took too many penalties."
Hedman put the Lightning ahead 1-0 at 19:57 of the first period with a power-play goal. Alex Killorn's shot deflected to Hedman near the right post, and he waited out Campbell until he slid out of position.
Vasilevskiy made a glove save on Timothy Liljegren from the slot at 1:26 of the second period to keep Tampa Bay in front.
"That's what you have to overcome to get to where we want to get to," Maple Leafs captain John Tavares said. "There's times when it goes great like Monday, when we really executed and everything was unflappable and we played a pretty darn good game. We had a pretty good first period (tonight), and obviously a tough break (on Hedman's goal) and then their goalie makes a good save."
Corey Perry made it 2-0 at 2:21 when he shot five-hole on Campbell on a breakaway after receiving a stretch pass from Hedman.
"It was probably maybe a little sigh of relief for our group (Hedman's goal), kind of trying to take the crowd out of it a little bit," Cooper said. "For me, the big one was the second one. It's all well and good to score one and then they tie it, but we get that second one and now you're making them chase."