Brook Lopez scored 17 points with a game-high 14 rebounds and Joe Johnson also supplied 17 points for the Nets, who clinched the Eastern Conference's final playoff spot on the last day of the regular season. Thaddeus Young added 15 points and 10 rebounds, and Jarrett Jack scored 13 off the bench.
Game 2 of the best-of-seven series is Wednesday in Atlanta.
Brooklyn's only lead of the game was 2-0. Atlanta led by as many as 16 points and held off several runs in the second half.
Hawks center Al Horford suffered a dislocated little finger on his right hand in the fourth quarter but had it taped up and returned to the game. He ended with 10 points and 10 rebounds.