Steven Stamkos had a goal and an assist, and Alex Killorn, Tyler Johnson and Nikita Kucherov scored for the Lightning (25-7-2). Vasilevskiy finished with 37 saves.
"We've got to be quick and assertive when you got the puck on your stick and anticipate your next play," Lightning defenseman Ryan McDonagh said. "We used our speed against them, and they did it to us too."
Killorn gave the Lightning a 1-0 lead when he beat Hellebuyck with a backhand at 13:01 of the first period for a power-play goal. Vasilevskiy got an assist after his long pass caught Winnipeg on a line change.
Perreault extended his goal-scoring streak to four games and tied the game 1-1 with a power-play goal at 19:43.
Winnipeg took a 2-1 lead when Tanev scored at 8:36 of the second, but Stamkos tied it 2-2 on a point shot 37 seconds later. Johnson made it 3-2 at 18:09, but Ehlers pulled the Jets even 3-3 at 19:19.
"I think it was an entertaining game for fans," Killorn said. "I know a lot of people were probably watching just because of where we stand in the East and where they stand in the West. I thought it was an entertaining game. Obviously, a lot of goals being scored. We don't want to allow that many, but it was a good game."
Kucherov put the Lightning ahead 4-3 with a power-play goal at 6:55 of the third period, extending his point streak to five games (two goals, four assists). However, Ehlers scored his second of the game at 14:23 to tie it 4-4.
"In the end," McDonagh said, "it's a stinging feeling for sure when you have a lead like that late on the road and can't find a way to close it out."