The Thunder had won 12 straight home games before falling victim to a team that improved to 3-1 under interim head coach P.J. Carlesimo.
Johnson scored a season-best 33 points while hitting five 3-pointers. Lopez had five rebounds to go with his 25 points and Deron Williams contributed 19 points and 13 assists for Brooklyn.
The Nets led by as many as 23 points in the first half, but Oklahoma City tied it in the fourth quarter. Brooklyn then closed the game on a 25-8 run. Oklahoma City slipped to 16-3 at home.
Oklahoma City's Kevin Durant scored 27 points, but was ejected from a game for the first time in his career. He picked up two technical fouls while Brooklyn was pulling away late in the contest.