The Oilers outshot the Kings 24-11 in the second period.
"Sometimes it's what the other team is doing, and they played a [heck] of a game," Kings coach Todd McLellan said. "They're figuring some things out over there and I thought we had a great first period. In the second period, we couldn't connect from one player to the next to get it going. We would just about connect, or we couldn't make the second play, and it countered and came back into our end."
Quick stopped Josh Archibald on a breakaway at 1:02 of the third period to keep it a one-goal game. Kailer Yamamoto came close to giving the Oilers a two-goal lead but hit the post at 4:46.
"I think they played a little better, they had more energy and more experience," Kings forward Phillip Danault said. "They played better as a team the last two games. We didn't play bad, but they played a little better. They had a little more power, and they were a little more ready, but we'll learn a lot from this and use it next year."
McDavid made it 2-0 at 16:07 on a delayed penalty when he collected his own rebound on a wrap-around attempt and scored on a backhand.
Smith made 11 saves in the third period for his second shutout of the series and sixth in the NHL playoffs.
"I think for our team that series pushed us in a certain way that made us grow," Oilers coach Jay Woodcroft said. "We learned a lot about ourselves over these last two weeks and the price that needs to be paid to have success at this time of year. I'm proud of our group and am looking forward to moving on to Round 2, whoever that is against."