The top seed in the Eastern Conference got early goals from four players -- none of them named Stamkos or Kucherov -- before holding off the New Jersey Devils for a 5-2 victory Thursday night in Game 1 of the first-round series.
Ondrej Palat, Tyler Johnson and Yanni Gourde scored, helping the Lightning build a 3-0 lead that New Jersey trimmed to one goal before Alex Killorn and Kucherov, who added an empty-netter with 1:12 remaining, finished off the win before a crowd of 19,092.
"Not the outcome we wanted," Devils goalie Keith Kinkaid said "That's why it's a series and not a game."
Taylor Hall scored an unassisted goal off a turnover in the second period, then assisted on Travis Zajac's power-play goal that trimmed the Devils' deficit to 3-2 midway through third against Andrei Vasilevskiy, who had 29 saves for Tampa Bay, which held off Boston in the final week of the season for the best record in the East.
For the Devils, a shaky opening period was too much to overcome.
"I don't know what happened. That's the way hockey goes sometimes. Starting on time is a big part of hockey, and especially playoff hockey," Hall said. "We have to be a team that's ready to battle right off the bat and just be aware that they have more than one line; more than Stamkos and Kucherov. They have a lot of dangerous guys and we have to be aware."
The line of Palat, Johnson and Brayden Point, matched up against New Jersey's top line, produced a pair of first-period goals and finished with six points.
Killorn's shot over Kincaid's glove restored a two-goal lead before Kucherov, who led the Lightning with 100 points this season, ensured there would be no comeback.
"I thought we played really well. I thought we played within our structure," said Johnson, who also had an assist on Palat's goal. "You've got to give Jersey credit. They pushed in that second period. That third period, I thought we took it back over. `If we continue to play like that, I like our chances this series."
Game 2 is Saturday at Amalie Arena.
Tampa Bay beat the Devils for the first time this year. The Devils won all three meetings between the teams during the regular season, with each game decided by one goal.
Kinkaid entered his first career playoff game as one of the hottest goalies in the league, going 7-0-1 over his last eight starts to help New Jersey grab its first playoff berth since the Devils reached the Stanley Cup Finals in 2012.
The Lightning, on the other hand, have been driven all season by failing to make the playoffs last spring after making deep runs previous two years.
With Kucherov and Stamkos leading the way, Tampa Bay paced the NHL in scoring and Vasilevskiy set a franchise record and tied for the league lead with 44 victories in his first season as a No. 1 goaltender.
But after reaching the Stanley Cup Finals in 2015 and coming within one victory of a return trip two years ago, this season ultimately will be judged on whether the Lightning can put together another strong bid to win it all.
"Last year was the first year that I missed the playoffs in any league. I've never had a long summer like that and that summer felt like forever," said Johnson, who has 22 goals in 48 career playoff games.
"So I'm glad where we're at right now. I'm excited to be back at this time," Johnson added. "It's the best hockey. It's the most fun you can play in."
While the Devils did a nice job of containing the high-scoring Kucherov and Stamkos, Palat, Johnson, Killorn and Gourde, who set a Lightning rookie record with 25 goals this season, showed why it's so difficult to totally shut down Tampa Bay's offense.
The momentum shifted on New Jersey's first power-play opportunity. Even though the Devils didn't score, they got off five shots against Vasilevskiy, who weathered the barrage before Hall broke through after Palat turned the puck over in the Lightning zone.
"We looked a little bit tentative, a little bit unsure, but I thought we settled into the game, particularly in the second period," Devils coach John Hynes said. "I thought the second half of the game was a little more of how we wanted to play. We'll regroup and we'll be a better team Saturday."
Stamkos returned to Tampa Bay's lineup after missing the final three games of the regular season with a lower body injury. ... It's the third time the Devils and Lightning have met in the playoffs. New Jersey won both previous series, advancing in the 2003 Eastern Conference semifinals in five games and ending a 2007 quarterfinal matchup in six. ... Zajac and captain Andy Greene are the only players remaining on New Jersey's roster from the Devils' 2012 postseason run.
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