TAMPA, Fla. -- Already short-handed on the offensive end of the ice, the Tampa Bay Lightning learned 90 minutes before Thursday's game that they would be without leading scorer Nikita Kucherov, who was sidelined due to an illness.

As they have throughout the second half of the season, the Lightning stepped up without their most talented players and still found ways to win, getting a 5-3 victory against the Detroit Red Wings at Amalie Arena to stay in the thick of the Eastern Conference wild-card chase.

"That's tough when you have a valued player like Kuch go down," said defenseman Andrej Sustr, who scored just his third goal of the season Thursday to help the cause. "It's happened all season, but the guys in this locker room are doing a good job of dealing with it and stepping up."

Tampa Bay (38-29-9) kept pace in a tight Eastern Conference wild-card race and picked up some distance on the New York Islanders, who went into the night a point behind Tampa Bay but lost to the Philadelphia Flyers.

The Lightning sit three points behind the Boston Bruins for the final playoff spot in the Eastern Conference.

The Lightning completed a five-game sweep of the Red Wings (31-34-12) this season, a first in their franchise history. While Detroit will miss the playoffs for the first time since 1990, the Lightning are still very much alive with six games remaining, thanks to another comeback.

"Two points, that's what I call it," Lightning coach Jon Cooper said. "We needed them, we got them. Now it's 'who's next?' That's all we've got."

Two power-play goals in the final five minutes of the second period were the difference in the game, with goalie Andrei Vasilevskiy getting 29 saves for the win. Unfortunately, Toronto and Boston also won to stay ahead of Tampa Bay, and Carolina won in overtime to stay just a point behind the Lightning.

Rookie Yanni Gourde, who had the game-winner in overtime in Monday's wild win against Chicago, added a goal in the third period, his third this season, and Detroit answered with a power-play goal from defenseman Mike Green to cut the lead to 5-3 with 11:42 to play.

Tampa Bay fell behind early, then used a strong second period to pull away to a 4-2 lead entering the final period, thanks to two late power-play goals.

Red Wings defenseman Danny DeKeyser, who had scored just his fourth goal of the season with 7:14 left to tie the score at 2, made two costly mistakes that led to Lightning goals on the power play.

On the first, Tampa Bay's Alex Killorn fired a shot that was stopped by Detroit goalie Petr Mrazek, but as DeKeyser went to clear the loose puck, he mishandled it and sent it straight into the net for a 3-2 Lightning lead with 3:47 left. That was credited as Killorn's 18th goal of the season.

DeKeyser was called for cross-checking with 2:18 left in the second and the Lightning again converted the power play. Jonathan Drouin stick-handled through the Red Wings' penalty-kill unit and fired a shot past Mrazek for his 21st goal of the season and a 4-2 lead with 1:56 to play.

Detroit jumped out to the early lead in a physical first period.

Frans Nielsen scored his 15th goal of the season with 15:38 left. Lightning defenseman Anton Stralman failed to clear a puck behind the net, and Darren Helm fired a quick pass to Nielsen in front of the net to beat Vasilevskiy for the 1-0 lead.

"I thought we came out pretty good," said Detroit's Henrik Zetterberg, who earned his 900th career point with an assist. "That first goal for them was a tough one, late in the first period for a little momentum. They scored a few more. I thought we had decent chances, but we had to work too hard for our goals."

That lead stood until nearly the final minute of the first, when J.T. Brown -- who had already served five minutes for fighting -- fired a shot between Mrazek and the right post for a 1-1 tie, just his third goal of the season.

"When we got the puck down to their end, we did some good stuff, created some chances," Nielsen said. "Offensively, we created enough tonight to score more goals."

Sustr got his third goal of the season for a 2-1 lead early in the second as Ondrej Palat's shot went off his skate and into the net.

That lead didn't last long, but the Lightning got the last two goals of the second.

The Lightning won despite playing a man down the entire game, with Kucherov joining four other key players -- centers Steven Stamkos, Tyler Johnson and Cedric Paquette and defenseman Jason Garrison -- out with injuries.

Kucherov leads the Lightning with 38 goals.

NOTES: Detroit RW Anthony Mantha left the game with an upper-body injury and did not return. ... Tampa Bay's Victor Hedman had the assist on Jonathan Drouin's goal late in the second period, and with that, set a Lightning record for points in a season by a defenseman with 66 this season. The record had been 65 by Roman Hamrlik in 1995-96. He has 15 goals and 51 assists on the season. ... Detroit played without C Luke Glendening, who missed his second straight game with a foot/ankle injury. C Ben Street was a healthy scratch. ... Tampa Bay recalled RW Joel Vermin from Syracuse, and he played nine shifts to help the short-handed Lightning front line.