Anthony Cirelli scored twice, and Brandon Hagel had two assists for the Lightning (43-21-4), who have won three in a row and four of five. Andrei Vasilevskiy made 26 saves.
The Lightning are second in the Atlantic Division, four points behind the Buffalo Sabres but with two games in hand.
McDavid scored his 399th NHL goal for the Oilers (34-28-9), who had points in three of their previous four (2-1-1). Connor Ingram made 22 saves.
"Absolutely, special teams were a big part of the story,” said Oilers coach Kris Knoblauch. “We had an opportunity to tie the game on the 5-on-3 with a minute-plus, two really good chances, one going off the goal post, then we can't give up that short-handed goal for the two-goal lead against the best defensive team in the League.
“Pretty tough to come back from that."
The Oilers are second in the Pacific Division, three points behind the Anaheim Ducks, who have two games in hand.
“We’re fortunate to play in this division,” McDavid said. “A lot of teams are fortunate to play in this division. It’s a bit of a pillow fight right now but we’re thankful not to have lost any ground.
“That being said, we have to find a way to win some games here on the road. We have to make up some ground.”
McDavid put the Oilers ahead 1-0 with 23 seconds left in the first period, tipping a wrist shot from the point by Evan Bouchard five-hole past Vasilevskiy.