Johnson finished with nine points on 4-of-11 shooting (1-of-6 from three), but his buzzer-beater propelled the Nets to their 11th win of the season. Oklahoma City is now 25-7 and has lost two straight at home.
However, the win wouldn't have been possible without Deron Williams, who took over down the stretch and finished with a game-high 29 points and five steals while shooting 10-of-17 from the field.
Paul Pierce added 18 points, four rebounds and three assists.
Brooklyn shot just 44 percent from the field in the win but outscored the Thunder, 29-16, in the game's final quarter and went on a 12-0 run to take a two-point lead with less than two minutes remaining.
As expected, Kevin Durant led the Thunder in scoring with 24 points, but he only attempted 13 shots on the evening. Three of his eight made field-goals came from beyond the arc.
Perry Jones III and Serge Ibaka scored 11 and 10 points, respectively, and were the only other OKC players to reach double figures.
Reggie Jackson managed just nine points on 4-of-13 shooting while Kendrick Perkins scored a season-high eight points and pulled down six rebounds in the loss.