Hedman's assist on the play was his 500th in the NHL.
"I am happy it came in a big game like this, late in the game. Those are the moments you live for, and it was a great feeling," Hedman said. "To do it for this club over the last 14 years is great, and a lot of credit goes to the guys that put the pucks in the net."
Cirelli had two goals and an assist, and Brandon Hagel had a goal and an assist for the Lightning (34-16-2). Andrei Vasilevskiy made 28 saves.
"I think [Vasilevskiy]'s the best in the League, next to my boy 'Jakey' (Oettinger)," said Stars goaltender Scott Wedgewood, who played for the Lightning's AHL affiliate during the 2019-20 season. "I've played with him, I've been on his team. I saw what he did for the Cup runs there to be a part of it. He's a workhorse. He just takes up a lot of the net and knows what works for him. He's a good dude, I like him a lot. It's fun to battle, but obviously I want to be on the other side of it."
Jamie Benn scored, and Wedgewood made 28 saves for the Stars (30-14-10).
Cirelli scored to give Tampa Bay a 1-0 lead at 10:13 in the second period. Hagel made a pass past defenseman Esa Lindell to spring Cirelli for a breakaway.
"It's easy playing with [Hagel] and [Alex Killorn], or it's [Steven Stamkos], or whatever it may be," Cirelli said. "Everyone's always in the right spot, they work so hard, they're good skaters, and good at making plays. When you get guys like that, it's easy to play. We've found a little chemistry the last couple games, so it's been going well."
Benn tied it 1-1 at 12:18 on a 3-on-1 rush.
"We were right there to at least get a point," Stars forward Luke Glendening said. "I thought [Wedgewood] was outstanding, and I thought for most of the game we played really well. It's a tough way to go."