Brayden Point and Ondrej Palat scored power-play goals 2:59 apart and Kevin Shattenkirk lit the lamp 54 seconds after Palat’s marker to help Tampa Bay build a 3-0 first period lead.
Nikita Kucherov drew the primary assist on both power-play goals to set a new Lightning record for points in a postseason. He has 28 points (6G/22A), two more than Brad Richards had in the 2004 Stanley Cup Playoffs, when the Lightning won the Cup.
Joe Pavelski scored a power-play at 14:43 of the second and Mattias Janmark picked up his first of the postseason 5:27 into the third as Dallas pulled within a goal.
John Klingberg and Alexander Radulov assisted on both of the Stars goals.
Andrei Vasilevskiy made 27 saves, including 17 in the second period when Dallas outshot the Lightning 18-5.
Anton Khudobin made 28 saves for the Stars.
Leon Draisaitl became the first German player to win the Hart Memorial Trophy as league MVP after leading the NHL in scoring with 110 points in 71 games. He also won the Ted Lindsay Award for most outstanding player as voted by his peers.
Connor Hellebuyck of the Winnipeg Jets won the Vezina Trophy as top goaltender, Nashville Predators blueliner Roman Josi claimed the Norris Trophy as the best defenseman, and Cale Makar of the Colorado Avalanche won the Calder Trophy as rookie of the year.