Steven Stamkos scored two power-play goals and Nikita Kucherov had two assists for the Lightning (1-3-0), who lost their home opener for the second straight season. Andrei Vasilevskiy made 21 saves.
"This is a stinger, we should never leave this game with zero points," Tampa Bay coach Jon Cooper said. "We probably should have left with two. It happens in this game. It happens when you play 82 games. Unfortunately, it's happening to us a lot early in this season, but this group should close that game out."
Stamkos gave the Lightning a 1-0 lead with a power-play goal at 1:25 of the second period when he connected on a one-timer from the left face-off circle off a pass from Vladislav Namestnikov. It was his fifth goal of the season.
Stamkos made it 2-0 at 4:12 with his second power-play goal, another one-timer from the left circle off a cross-ice pass from Kucherov.
He has seven points (six goals, one assist) in four games.
"I think we just lacked some urgency," Stamkos said. "We can't take for granted that what we've done in the past with leads, especially on home ice, that everyone can fall back and it will be ok. It's got to be urgent hockey. We have to make safe, sound plays. We definitely made some uncharacteristic plays in that regard."