Tanner Jeannot scored at 17:04 to make it 3-0 when he put in a rebound off a shot by Michael Eyssimont.
"We know what we need to do to be successful, and we've been working on being smarter with the puck in the neutral zone," Jeannot said. "I think we've done a good job of that the past two games. [Vasilevskiy] has looked like the best goalie in the world. We just have to keep building our game and help him out."
Guentzel scored with 53 seconds left in the third period for the 3-1 final when his shot went in off the skate of Lightning forward Nicholas Paul after Vasilevskiy misplayed the puck behind the net.
"I thought we had opportunities, especially in the 1st period, to put pucks at the net and we didn't," Penguins coach Mike Sullivan said. "We're looking for lateral plays and they never materialized. We're trying to encourage them to put the puck at the net more."
Pittsburgh continued its slump on the power play, going 0-for-4, including a two-man advantage for 39 seconds with 4:08 left in the third. The Penguins have failed to score on their past 34 power plays.
"I don't think we're necessarily trying to be too cute, if anything maybe a little hesitant," Pittsburgh captain Sidney Crosby said. "We've got to play on our toes a little more.
NOTES: Penguins forward Bryan Rust left the game late in the second period. Sullivan said he was being evaluated for an upper-body injury. ...Crosby got his 964th assist, tied with Doug Gilmour for 14th in NHL history. He won 19 of 27 face-offs (70.4 percent). ... Guentzel had a game-high 14 shot attempts (five on goal). ... Cirelli has three goals in the past two games after scoring just twice in November. ... Lightning defenseman Mikhail Sergachev blocked seven shots in 24:17 of ice time.