Leon Draisaitl and Kailer Yamamoto each had a goal and an assist for the Oilers, who have won two in a row and moved into third place in the Pacific Division. Tyson Barrie added two assists.
''Tonight was a total team win, contributions up and down the lineup,'' Oilers coach Jay Woodcroft said. ''In the two games as a whole against Tampa we gave up 55 shots against the Stanley Cup champions. We did a good job defensively in both games.''
Zach Bogosian scored for the two-time defending champion Lightning, who have lost three in a row for the first time this season. Brian Elliott finished with 45 saves.
''When things aren't going well for you, you invent ways to shoot yourself in the foot,'' Tampa Bay coach Jon Cooper said. ''Whether it's turnovers, taking too many penalties, we're finding ways on this road trip to make it hard on ourselves. If you're going to take that many penalties and you're going to put some of the best players in the world on the ice all night, it's going to be tough for you.''
Edmonton managed to get a rare first goal of the game midway through the first period when McDavid stripped a puck and danced around Victor Hedman at full speed before tucking it past Elliott.
The Oilers improved to 18-0 when scoring first this season.
''I'm not sure what it is. I think we just find a comfort level in our game,'' McDavid said. ''Obviously the start is important. We haven't found a way to get the first goal too many times, so when we do we have to bear down and find a way to get a win.''
The Oilers came close to extending their lead seven minutes into the second, but Warren Foegele rang a shot off the crossbar - the second time in the game Edmonton hit a crossbar.
They made it 2-0 with 44 seconds left in the middle period as McDavid picked the top corner for his 32nd of the season, also taking the league lead for points with 83.
''I think we had an all-around effort,'' Draisaitl said. ''The PK was really good. I think our power play could have been sharper, but we did score a big goal to make it 2-0 at the end of the second there. You have to find the right time to score sometimes too. We did that and, 5-on-5, I thought we were really solid.
''I think we are finding our gear here a little bit and taking steps in the right direction.''
The Lightning finally got on the board midway through the third as Bogosian was left alone in the slot and sent his third of the season over Koskinen's shoulder.
After killing off a lengthy 5-on-3 Tampa power play, the Oilers regained their two-goal lead three minutes later as Draisaitl had a long breakaway before depositing his 39th of the campaign through Elliott's legs.
Yamamoto added an empty netter to put the game away for Edmonton.
NOTES: It was the first time the Lightning have played at Rogers Place in Edmonton since they won the Stanley Cup in the ''bubble'' in 2020. ... Oilers forward Josh Archibald made his season debut after he was diagnosed with myocarditis at training camp following a bout with COVID-19. Archibald remains unvaccinated, meaning he cannot currently travel with the team. ... Still out with injuries for Edmonton were Ryan Nugent-Hopkins (upper body), Kris Russell (undisclosed), Jesse Puljujarvi (lower body) and Kyle Turris (upper body).
Lightning: At Vancouver on Sunday night.
Oilers: Host Detroit on Tuesday night.
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