Sergachev gave the Lightning a 2-1 lead at 10:21 of the third period. With four seconds remaining on the power play, the defenseman scored with a shot to the near post with Corey Perry providing the screen.
"They get two power-play goals tonight, we get none," Larkin said. "That's kind of the story of the game."
Stamkos made it 3-1 with an empty-net goal at 19:58.
"I don't think we, to a man, put out the effort that we wanted to [against the Penguins]," Elliott said. "Winning one at home before you go on the road for a while is a good feeling. Sometimes all you need to get on another little run is that good feeling when you come off the ice."
NOTES: The Lightning have not lost consecutive games in regulation this season. ... Sergachev has scored two goals in the past three games after not scoring in his previous 40. ... Seider has scored 12 points (one goal, 11 assists) during his eight-game point streak. He is the first Red Wings rookie to have an eight-game point streak since Steve Yzerman in 1983. ... Red Wings forward Carter Rowney left the game early in the second period with a lower-body injury.