BUFFALO, N.Y. -- The Tampa Bay Lightning got the hot start they were looking for Thursday night. Their goaltender made sure it held up.

The Lightning jumped out to an early 3-0 lead in the first period, and goalie Andrei Vasilevskiy stopped 20 shots in a frantic second period to lead Tampa Bay to a 4-1 victory.

"It was a weird game," Lightning coach Jon Cooper said. "But it's just a consistency (issue). ... I think we played like they were going to lay down (in the second period) and you can't do that in this league and our goalie bailed us out for the win."

Centers Steven Stamkos and Tyler Johnson, right winger Nikita Kucherov and defenseman Victor Hedman scored for the Lightning (7-6-2). Vasilevskiy made 30 saves.

Center Jack Eichel scored for the Sabres (5-8-0).

Sabres starting goalie Linus Ullmark surrendered three goals on 11 shots in the first period and was replaced by Chad Johnson, who stopped all 10 shots he faced.

After Tampa Bay struggled to find offense during a recent skid -- five losses in the previous six games -- the Lightning came out flying against the Sabres.

Stamkos opened the scoring 5:55 into the game following a defensive breakdown in the Sabres' zone. Center Vladislav Namestnikov found a wide-open Stamkos on a cross-ice pass to his left, and the Lightning captain buried a slap shot from the left circle for his seventh goal of the season.

Johnson made it 2-0 less than six minutes later. Center Alex Killorn found Johnson on the inside edge of the right circle with a backhand pass, and Johnson fired a wrist shot to the blocker side at 11:35.

Kucherov increased Tampa Bay's lead to 3-0 with 1:40 left in the period on a gritty goal from beside the Sabres' net. After taking a hit from Buffalo defenseman Rasmus Ristolainen, Kucherov deposited a rebound into the net while falling to the ice. It was his fifth goal of the season.

With just seven goals in the past six games, the fast start was exactly what the Lightning needed.

"We're so used to being able to score and now when we do score it's like, 'Holy cow, boys, look what we just did,'" Cooper said. "We've got to wipe that mindset away."

They relied heavily on Vasilevskiy after that. The Sabres came back hard, putting 21 shots on net in the second period. Vasilevskiy stopped all but one, a standout goal from rookie Eichel.

"First period, middle. Second period, it's hard," Vasilevskiy said. "Moments, scrambles, screen shots, but that's my work. I don't have to come into locker room and say, 'Oh my gosh 21 shots'. This is my work. Just one more day."

Said Cooper: "You need your goalie to bail you out, but he was the best player on the ice for us and we can't keep depending on our goaltending."

Hedman added an empty-net goal with 30 seconds remaining.

Eichel's goal was a beauty. The budding superstar moved away from Tampa Bay defenseman Andrej Sustr with a spin move along the left wall near the blue line before skating up ice. After some nifty stickhandling inside the left circle, Eichel snapped a hard wrist shot to the glove side for his fifth goal of the year.

"I just wanted to kind of push the defense back," Eichel said. "I think he tried to step up on me on my left side and I was able to turn him my other way and get in for a shot."

Sabres coach Dan Bylsma was pleased with Buffalo's comeback effort, but not with the disappointing start.

"We gave a good team too many easy opportunities to score," Bylsma said. "They took heavy advantage of it. Some checking assignments and missed plays ... we hung our goalie out to dry with those opportunities.

"If we had played the whole game like we played the second period and the third period, we would've been fine."

NOTES: D Carlo Colaiacovo and C Tim Schaller were scratched for the Sabres. ... D Matthew Carle, LW Jonathan Drouin (lower body) and LW Tye McGinn were scratched for the Lightning. McGinn missed a chance to play against his brother, Jamie McGinn. McGinn is a left winger for the Sabres. ... C Cedric Paquette returned for the Lightning after missing five games with an ankle injury. ... This was the third of four meetings between the Sabres and Lightning this season. Their fourth and final meeting takes place on Tuesday in Tampa Bay. This marks the second of eights sets of home-and-home games for the Sabres this season.