Zach Bogosian scored, and Brian Elliott made 45 saves for the Lightning (37-15-6), who have lost three straight in regulation for the first time this season.
"We were grinding and sticking with it, but definitely making it hard on ourselves by taking a lot of penalties tonight," Lightning defenseman Ryan McDonagh said. "When you give their top-end guys a lot of puck touches and a lot of time and space, they're going to gradually get more confidence as the game gets on. It's on us to be better disciplined there and that will definitely help our chances moving forward."
McDavid gave the Oilers a 1-0 lead at 10:02 of the first period. He skated around Lightning defenseman Victor Hedman on a rush down the right side, cut across the net and tucked the puck in past Elliott. Edmonton is 18-0-0 when scoring the first goal 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. I thought we did a good job of that tonight."
McDavid made it 2-0 on the power play at 19:15 of the second period on a shot from the left face-off circle.
"When things aren't going well for you, you invent ways to shoot yourself in the foot," Lightning 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."