Shai Gilgeous-Alexander, the reigning NBA Most Valuable Player and finalist for the award this season, scored 22 points and the Thunder capitalised on 21 Lakers turnovers to hand LeBron James a defeat in his 300th career playoff game.
Eastern Conference top seeds Detroit are also up 2-0 after a 107-97 home win over the Cleveland Cavaliers.
In Oklahoma City, Gilgeous-Alexander was again below his best but he was amply supported.
Chet Holmgren scored 22 points and pulled down nine rebounds, Ajay Mitchell added 20 points and Jared McCain delivered 18 points off the bench to help the Thunder withstand a 31-point performance from Austin Reaves.
James, who became the first player to contest 300 post-season games, scored 23 points and handed out six assists, and the Lakers led by five points early in the third quarter.
But with league-leading scorer Luka Doncic still sidelined by injury the Lakers couldn't hang on, even with Gilgeous-Alexander on the bench for considerable stretches because of foul trouble.
Oklahoma City produced a 22-5 scoring run to seize control and will aim to keep the pressure on when the series shifts to Los Angeles for games three and four on Saturday and Monday.
"We've got to be the aggressor," Gilgeous-Alexander said. "I feel like they were playing with more force, they were attacking harder, making quicker decisions, playing with a better sense of urgency, especially in the first half.
"As long as we take care of that we should have our foot in the right direction."
A bruising contest saw both teams irked by the officiating. Gilgeous-Alexander was whistled for a flagrant foul and both he and James were spent sprawling under the basket after a foul by Reaves late in the game.
Lakers coach JJ Redick took issue with the officiating, saying the Thunder "have a few guys who commit a foul on every possession".
But he added: "We didn't lose because of the refs."
