After leading 26-14 in the first, the Nets were outscored in both the second and third before edging out the Heat in the final quarter 26-22.
Joe Johnson paved the way for the Nets with 19 points during 33:03 on the court. Marcus Thornton was second on the team with 16 points off the bench.
Brooklyn shot 52.9 percent from the field during the game and is now 19-1 when it shoots 50 percent or better.
What's Next: Brooklyn will return to the court on Wednesday when it travels to Orlando to take on the Magic at 7:00 p.m.