Stamkos gave the Lightning a 1-0 lead on a power play at 1:07 of the first period, one-timing Nicholas Paul’s feed in the left face-off circle.
Tyler Motte made it 2-0 at 7:15 when he backhanded a rebound in front for his first goal in 21 games this season.
Darnell Nurse cut it to 2-1 with a short-handed goal at 1:23 of the second period when he took a pass from Nugent-Hopkins and scored with a wrist shot.
McDavid tied it 2-2 on a power play at 7:20, scoring right after a face-off in the right circle to extend his point streak (27 points; seven goals, 20 assists).
Zach Hyman gave Edmonton a 3-2 lead with a power-play goal at 10:02 on a redirection of Bouchard’s slap shot from the right point.
Bouchard has 20 points (five goals, 15 assists) during his point streak.
The Oilers outshot the Lightning 23-7 in the second before giving up five goals in the third.
“I thought for the most part that we played a solid game, but we obviously gave up a couple too many goals,” Edmonton forward Leon Draisaitl said. “I thought we were the better team and probably deserved to win, but it is obviously not the way that the League works.”
Stamkos tied it at 6:48 of the third, batting Haydn Fleury’s rebound out of mid-air to make it 3-3.
Kucherov put Tampa Bay back in front 4-3 at 12:47, sliding it under Skinner’s pad, and Stamkos beat Skinner glove side at 14:02 to make it 5-3.
“He shot it from the blue line today and scored because their goalie got screened a little bit. Anywhere he shoots it from, he’s got a chance,” Lightning defenseman Mikhail Sergachev said of Stamkos, who had seven shots on goal. “I always think that he needs to shoot more and more.
“He’s got to shoot 10 times in a game and he’s going to score two. He’s got a very accurate shot, and he’s been in the League for 15 years being a leader on this team and he’s just a threat out there.”