Vladimir Tarasenko had a goal and an assist, and Filip Gustavsson made 19 saves for the Wild (40-20-12), who remained five points behind the Dallas Stars for second place in the Central Division.
"It's unfortunate because I thought we played a decent road game," Minnesota forward Nick Foligno said. "Would've liked to have won the special teams battle. We did a lot of good things, but just an unfortunate bounce (on Cernak’s goal). If we play like that more times than not we're going to give ourselves a chance to win."
Cernak put the Lightning ahead 4-3. After Tampa Bay defenseman Charle-Edouard D'Astous sent the puck down the ice, Gustavsson couldn't control it on the bounce off the end boards, and it trickled through his legs at the left post, allowing Cernak to knock it in from the top of the crease.
"We had a goal that we had to win tonight, so this was huge," Cernak said. "They had a great start with two power-play goals and we knew we had to play better. We started putting pucks on the net, we were pressuring them and making the right plays."
Hagel scored into an empty net to make it 5-3 at 18:42, and Pontus Holmberg was awarded an empty-net goal at 19:36 that made it a 6-3 final when he was taken down by Brock Faber on a breakaway.
Mats Zuccarello gave Minnesota 1-0 lead with a power-play goal at 2:28 of the first period when his pass attempt from the left face-off circle deflected in off the skate of Tampa Bay defenseman Ryan McDonagh on the far side.
Faber extended the lead to 2-0 with a power-play goal at 18:49 when his point shot through traffic deflected off the bottom of Vasilevskiy's glove.
"The [power play] is dangerous and both units scored big goals," Foligno said. "It's fun to see how dangerous and lethal they could be because this time of year you need your special teams to be clicking."
Brayden Point scored on the power play to make it 2-1 at 5:45 of the second period. He took a feed from Hagel and scored from above the left hash marks to the short side.