Brooklyn raced to as much as a 21-point lead in the fourth period after the Nets had been only one in front at the end of the first half.
Johnson hit 10-of-16 from the field and made two of Brooklyn's 11 3-pointers on his way to 22 points. Gerald Wallace added 10 for the Nets and Andray Blatche had 14 points and nine rebounds.
Brooklyn went 11-of-of-20 from beyond the arc while Orlando hit just 1-of-11.
It was the third consecutive loss for the Magic, who came up with 16 points from Glen Davis.