TAMPA, Fla. -- Lightning coach Jon Cooper knew his team was in for a daunting opening week, but Tampa Bay closed out that span emphatically.

The Lightning held on for an impressive 5-4 win against the defending Stanley Cup champion Pittsburgh Penguins on Thursday at Amalie Arena.

"They've won back-to-back Cups. They're a pretty good team over there," said Cooper, whose team improved to 3-0-0 at home. "Any time you can beat them, that's a win for us. We didn't beat them last year ... I thought it was imperative that we get out to a good start. It's a little bit of a barometer for our team."

Tampa Bay (3-1-0) was swept in three meetings with Pittsburgh (2-2-1) last season, but the Lightning beat Penguins goalie Antti Niemi for five goals on Thursday.

Steven Stamkos scored his first in 11 months, Victor Hedman scored with 0.1 seconds left in the first period, defenseman Slater Koekkoek scored the first two goals of his NHL career, and Alex Killorn added four assists in an eventful win for the Lightning.

"I knew it was a matter of time," said Stamkos, who had five assists in the first three games of the season but no goals until Thursday. "I wasn't losing any sleep over it. I'm happy to be playing hockey again and part of some wins here."

Pittsburgh, down 5-3 entering the third and playing the second half of a back-to-back, got a goal on a rebound by defenseman Matt Hunwick (his first) with 9:59 left, but Tampa Bay goalie Andrei Vasilevskiy held on for the win. Vasilevskiy made 36 saves, the biggest when Jake Guentzel had a breakaway to potentially tie the game with seven minutes left.

"Have we put up unbelievable defensive gems? We haven't," Cooper said. "But we've won these games, and I know that part of our game will round into shape. I liked our compete, I liked our fight. There are so many things I liked about the game."

Penguins defenseman Justin Schultz liked the game's frenetic pace but wasn't pleased with his club's defensive letdowns.

"Too many Grade A chances for them," Schultz said. "I thought we did a good job of battling all night. It was a tough back-to-back for us, and we had lots of chances in the third to tie it."

The Lightning led by two after a wild second period that saw the teams combine for five goals. Stamkos scored a power-play goal with 16:11 left in the second for a 3-1 lead. Pittsburgh answered with 11:02 left, as Chad Ruhwedel fed a pass to Conor Sheary, who beat Vasilevskiy on a breakaway for his third goal of the season, cutting the lead to 3-2.

"It's definitely nerve-racking," Sheary said of the game's fast pace. "It's kind of the style, with 40 shots a side and lots of scoring chances each way."

Less than a minute later, Tampa Bay's Nikita Kucherov fired a shot to the top right corner of the net for his fourth goal in as many games and a 4-2 lead with 10:11 left. Pittsburgh answered again, with Bryan Rust getting his first goal on a power play, converting the rebound of a shot from Olli Maatta.

The Lightning killed off another Pittsburgh power play, and as Koekkoek came out of the box, he set up a breakaway. Killorn fed Koekkoek for a backhand goal, his second of the night. Killorn had assists on four of the Lightning's first five goals.

Tampa Bay led 1-0 on Koekkoek's first career goal, then saw Pittsburgh tie it later in the first period on a power-play goal by Guentzel (his second). Guentzel redirected a wide shot from Kris Letang. The Lightning had a buzzer-beater to grab the lead back, getting a power-play goal from Hedman (his first).

NOTES: The Lightning, continuing to carry eight defensemen, had D Andrej Sustr as a healthy scratch, as well as C Cedric Paquette (undisclosed) and RW J.T. Brown. ... Pittsburgh had LW Scott Wilson as a healthy scratch for the second straight game, along with RW Josh Archibald and D Chris Summers, who have yet to play this season. ... Tampa Bay closes a three-game homestand Saturday against the St. Louis Blues, while Pittsburgh returns home to host the Florida Panthers on Saturday.