Johnson finished with 28 points and five assists, while Gerald Wallace, who had an offensive rebound and putback in regulation to force the first overtime, had 25 points. He and Johnson both played more than 50 minutes.
Brook Lopez returned to the Nets' lineup for the first time in seven games. He played 24 minutes and scored nine points.
The Pistons trailed by as many as 17 points in the first half. They cut the deficit to 12 by halftime and then out-scored the Nets 30-14 in the third quarter to take a lead into the fourth.
Brandon Knight scored 22 points to lead five Pistons in double figures. Rodney Stuckey scored 19 points off the bench, Greg Monroe had 17 points, Jason Maxiell had 13 points and Prince scored 12 points.
Kyle Singler, who scored eight points, had an offensive rebound and put-back to tie the game on the possession before Johnson hit the game-winner.