Alex Killorn and Cedric Paquette scored for the Lightning (5-3-1), who have won three of their past four games.
Guentzel and Brandon Tanev scored, and Tristan Jarry made 45 saves for the Penguins (6-5-0), who have lost three in a row, including 4-2 to the Florida Panthers on Tuesday.
"[Tristan] played really well for us, he made some big saves," coach Mike Sullivan said. "I thought we played really hard, you know, against a team that's a pretty deep team. This is another game that could've went either way, it didn't go our way. That's two nights in a row now."
Hedman scored the winner with a shot from the center point off a pass from Steven Stamkos with Guentzel in the penalty box for holding. It was the second Tampa Bay power play in the final 4:41 of the game.
"It was obviously a little frustrating being down a goal going into the third," Hedman said. "We're a resilient group and we find ways to win. Today, the power play came through."
Killorn gave the Lightning a 1-0 lead at 9:46 of the first period when he redirected a shot by Nikita Kucherov for his first goal of the season.
Tanev tied the game 1-1 with a high backhand shot at 5:06 of the second.
Guentzel made it 2-1 when he scored off a touch pass from Crosby at 19:01 of the second. It was Crosby's 1,230th NHL point, moving him past Norm Ullman for 40th in NHL history.
"We were right there, back-to-back nights we get a lead," Crosby said. "Unfortunately, you've got to kill all those penalties."
Paquette tied it 2-2 at 7:07 of the third with his first goal of the season. He missed the first eight games of the season with an upper-body injury.
"[Paquette] is an extremely important player for us," Lightning coach Jon Cooper said. "For him to come back the way he did, he just brings an identity to his line."
