NEW YORK (AP) - Joe Harris had 16 points and Spencer Dinwiddie added 15 off the bench for the Nets, who last won five straight March 25-April 2, 2015.
Atlanta cut Brooklyn's 21-point lead down to 66-64 when Kent Bazemore capped a 6-0 run with two free throws late in the first half.
The Nets pulled away in the third quarter with an 11-5 run to make it 108-82.
John Collins scored 29 points and Dewayne Dedmon had 24 points and 12 rebounds for the Hawks, who have lost three straight and seven of their last eight.
Hawks: Rookie point guard Trey Young had 13 points and 10 assists.
Nets: The Nets had their highest scoring game ever at the Barclays Center, topping the 131 they scored against Philadelphia on March 15, 2016. ... Brooklyn has posted at least 70 points in the first half of its last two games, a feat it had not accomplished since the 1983-84 season. The Nets scored 70 points through two quarters against Washington on Friday and had 72 at the half against Atlanta. ... The Nets have scored at least 100 points through the first three quarters in consecutive games for the first time in franchise history.
New York Yankees radio play-by-play man John Sterling called Sunday's Nets broadcast on the YES Network. Sterling, who has called every Yankees radio game since 1989, was the voice of the Nets from 1975 to 1980. He moved on to the Washington Bullets the following season before switching over to play-by-play duties for Atlanta from 1981 to 1989 prior to joining the Yankees radio booth.
Former Nets guard Jeremy Lin returned to Brooklyn and said he wished things had ended differently. Lin was surprised and upset with the trade that sent him to Atlanta on July 12 after two years and just 37 games in Brooklyn due to injuries.
"Honestly, coming in the building, just thankful," said Lin, who was averaging 10.8 points and 41 percent shooting from the 3-point line in 25 games. "As sad as it is when I think of Brooklyn, obviously, I just think of a lot of injuries and things like that. It's quite a contrast to being healthy, being able to participate in a game."
Hawks: Host the Washington Wizards on Tuesday night.
Nets: Host the Los Angeles Lakers on Tuesday night.