TAMPA, Fla. -- Down two goals early, the Tampa Bay Lightning didn't panic in Thursday's opener, then struck for three goals in the final period to rally to a 6-4 win over the Detroit Red Wings at Amalie Arena.

"One of the staples of our team, where we've grown since I've been here, is just the calm on the bench," Lightning coach Jon Cooper said. "We've seen this before. This happens in games. They were a resilient group ... We felt like we were playing good, and then special teams took over after that."

Tampa Bay (1-0-0) tied the game early in the third, then took the lead 4-3 on a power-play goal by Tyler Johnson, five seconds after Detroit (0-1-0) was called for a substitution penalty for having too many men on the ice. The Lightning added another power-play goal in the third, again for Detroit having too many men on the ice.

"We still should know that rule and not have six guys on the ice," Detroit's Henrik Zetterberg said of struggles in a season opener. "It's something that we have to fix for Saturday (at Florida)."

Tampa Bay's power play, which was the NHL's fifth-worst last year, converting at 15.8 percent, struck for three goals in Thursday's win. The go-ahead goal came five seconds into one advantage, as center Steven Stamkos fired a pass that was redirected in front of the net to beat Detroit goalie Petr Mrazek. Tampa Bay added a third power-play goal with 2:59 left on a goal by center Alex Killorn.

Detroit started this season where it finished last year, as the Lightning had eliminated the Red Wings in the opening round of the playoffs for the second year in a row. Goalie Ben Bishop, who had shut out Detroit in last year's clinching Game 5, simply outlasted Mrazek on Thursday as two teams tried to shake the rust off their defenses in the season opener. Bishop became the Lightning's career saves leader during the win as well.

Down 5-3 late, the Red Wings scored on a long shot by Danny DeKeyser that caromed off a stanchion and got past Bishop to get Detroit back within a goal with 2:05 left. Tampa Bay answered with an empty-net goal from Valtteri Filppula with 1:21 remaining for the final score.

The Lightning, twice down two goals, rallied back to tie the game at 3-3 with 16:43 left in the third period, as center Brian Boyle fired a shot to the top left corner of the net, past Mrazek.

Red Wings defenseman Jonathan Ericsson got a game misconduct penalty and was whistled as the instigator in a fight with 6:36 left in the game that resulted in 24 minutes of penalties but no power play.

Detroit's first three goals came from newcomers making their Red Wings debuts -- two goals in the first nine minutes of the game from left winger Thomas Vanek, including one on the Red Wings' first shot of the season, on a power play just 3:12 into the game.

Lightning defenseman Nikita Nesterov turned the puck over deep in his own zone and Detroit capitalized, with Gustav Nyquist feeding a pass to Vanek for a 2-0 lead with 11:34 left in the first.

"We were down 2-0 there, but in the first period, we had the majority of the chances and we started to build in the last 10 minutes," Johnson said. "We have a lot of confidence in this team. We've been through a lot together, we've been down before and come back before. I don't think anyone was too worried."

Tampa Bay answered with a power-play goal with 12:37 left in the second, as Jonathan Drouin flipped a shot past Mrazek to the near top corner of the net. Less than a minute later, Detroit extended its lead to 3-1 as center Frans Nielsen, making his Red Wings debut, poked in a loose puck past Bishop with 11:42 remaining.

"We killed some big penalties there in the first, got a power-play goal right away -- there were some good things," Zetterberg said. "We have stuff that needs to be better and we'll take care of that tomorrow."

The Lightning again pulled within a goal, as center Cedric Paquette fired a shot between Mrazek's legs to make it 3-2 with 6:55 left in the second.

NOTES: The Lightning's lone healthy scratch was D Slater Koekkoek. Detroit had only two players scratched in D Ryan Sproul and C Andreas Athanasiou. ... The Red Wings assigned their third goaltender, Edward Pasquale, to the Grand Rapids Griffins of the AHL before Thursday's game. ... The Lightning open the season with only one key player sidelined by injury, as RW Ryan Callahan remains out as he recovers from hip surgery he had in June. ... Detroit is without four injured players to start the season -- C Joe Vitale and RW Johan Franzen have concussions, D Niklas Kronwall has a knee injury and RW Tomas Jurco a back injury.