ATLANTA — The Nets said they wanted another trip down to Atlanta, another shot at the Hawks. And this time they got their payback.

In a back-and-forth affair, Brooklyn had the final forth. The Nets outlasted Atlanta 114-113 before 15,906 fans — and what felt like that many lead changes.

It was Mikal Bridges — who had a game-high 32 points, six assists and five rebounds — that hit the go-ahead basket with five seconds left, and Dennis Smith Jr.’s defense forcing Hawks star Trae Young into a last-ditch miss that made it stand up as the game-winner.

This instant classic had 43 lead changes, the most in any game since play-by-play was first tracked (back in 1996-97), according to Elias Sports Bureau.

And Bridges provided the final one, clasping best friend Cam Johnson in a hug afterward and holding up one finger in celebration — symbolizing their first-ever career road win over the Hawks.

“Oh my God, first win in Atlanta,” Bridges said. “Took six years, took six years. Took me to get to the East so I guess that’s God’s way of telling me, ‘OK, you can’t just play once a year you gotta at least come here twice.’ Just so happy to get this dub.”

It was Brooklyn’s fifth win in the last six games — ever since its defense had bottomed out in a 147-145 overtime loss here two weeks ago.

The Nets had openly hoped to see the Hawks scheduled as one of their games added for missing the In-Season Tournament quarterfinals. They got their wish — and the win.

“Really, I was telling myself ‘We’re gonna get this one,’ ” Jacque Vaughn said. “I can literally remember saying to myself, ‘We’re going to get this one.’ So that feels good, that I believe in our group that somehow we were going to figure it out.”

They did just that.

Off an inbounds play, Bridges hit a go-ahead layup off a feed from Spencer Dinwiddie with 32.8 seconds left. And after Dinwiddie forced Young into a miss on the other end, he grabbed the defensive rebound and got fouled.

Dinwiddie — who had just two points on 1 of 10 shooting through three quarters, but had 11 in the fourth on 4 of 9 — sank just one of two free throws, leaving Brooklyn ahead 112-110. Young, who hit a buzzer-beater to down the Nets last season, then had 43 against them two weeks ago, hit a 3 over Smith’s outstretched arms.

But Vaughn didn’t call a timeout, letting Bridges attack in transition. He got to his midrange and hit an 18-footer with 5.1 seconds left in regulation. Smith’s defense ensured there would be no overtime, no gut-wrenching loss. Just a Brooklyn victory.

“They ain’t call no foul. That’s all it was,” Smith said. “Thankfully. It was a tough shot. He missed.”

Young finished with 30 points and nine assists.

But Bridges came into the game tied with Young for the second-most clutch points in the league this season behind only Damian Lillard. The Nets star had 10 points in the fourth quarter on 5 of 6 shooting, guarding Young for much of the contest and helping Smith on him on the final, fateful play.

“Growing up playing basketball, you want to be in those situations where it comes down to last possessions, getting a stop and scoring. So everybody’s just locked-in and wants to win,” Bridges said. “That’s all I care about. That could’ve been my second point of the game, if I hit that game-winner, but I just want to come out here and get this win.”

The Nets (11-9) got double-digit rebounds from both Nic Claxton and Day’Ron Sharpe.

This was a nerve-wracking seesaw affair, but the kind that shows their turnaround might be more epiphany than just aberration.

“It was basketball, and you gotta love it,” said Johnson, who had 17 points. “You gotta love it. You gotta love the back-and-forth basketball games where you’re just throwing blows back-and-forth. Those are the moments you love as a competitor.”