ATLANTA — The New York Yankees took their time scoring against the Braves.

Then they got an unlikely home run — and a long-awaited offensive boost from Alex Rodriguez.

Francisco Cervelli hit his first career homer to break a 14-inning drought in Atlanta, then Rodriguez came through with a two-run single that sparked the Yankees to a 8-4 victory over the Braves on Wednesday night, snapping New York’s three-game losing streak.

Joba Chamberlain (4-2) went 6 1-3 innings, giving up two earned runs for his first win in four starts. After Jeff Francoeur’s two-out single in the eighth made it 6-4, the Yankees called on closer Mariano Rivera with the potential tying runs on base. He struck out Kelly Johnson and worked a scoreless ninth for his 498th career save and 16th this season.

Atlanta had pitched two straight shutouts, having blanked the Chicago Cubs in a makeup game Monday before beating the Yankees 4-0 on Tuesday. The Braves stretched their scoreless streak to 23 innings with a 1-0 lead through five despite losing starter Kenshin Kawakami, who was struck at the base of the neck with a liner in the third.

The injury wasn’t serious, but Kawakami didn’t return.

Kris Medlen kept the streak going for another two innings — in fact, the Yankees hadn’t even mustered a baserunner. But the visiting team, cheered on by a huge contingent of New York fans, finally broke through in the sixth.

Medlen (2-3) walked leadoff hitter Brett Gardner, who was promptly picked off on a disputed call. Manager Joe Girardi raced out to argue with first-base umpire Bill Welke — television replays showed the Yankees had a legitimate beef — and wound up getting tossed.

That seemed to fire up New York.

Cervelli, the team’s No. 2 catcher, got the start after Jorge Posada struck out four times Tuesday and came through with his homer into the first row of seats in left, evening the score at 1. After Chamberlain lined out, Derek Jeter singled to left, Johnny Damon lined a single to center and Mark Teixeira walked to load the bases.

The Braves brought on Jeff Bennett to face Rodriguez, having a miserable season since missing the first month with a hip injury. He was batting just .204 and quickly fell behind 0-2 in the count. Bennett barely missed the strikeout when Rodriguez fouled a pitch off the glove of catcher Brian McCann, who stared at his empty mitt in disgust.

Rodriguez lined the next pitch — a fastball over the inside corner — into right-center for a two-run single. Clearly relieved, he clapped his hands and exchanged a slap with first-base coach Mick Kelleher.

Nick Swisher led off the seventh with a homer, stretching New York’s lead to 4-1. Swisher wasn’t in the original lineup posted in the Yankees clubhouse. Instead, Melky Cabrera was listed as the starting right-fielder, but that was merely a mistake.

The Yankees put up the correct lineup — this one with Swisher in it — and benefited from both a long ball and a great catch crashing against the wall in right that kept the Braves from coming all the way back. Turning three different ways, Swisher looked back in time to catch Nate McLouth’s drive, keeping him to a sacrifice fly that made it 4-3.

New York restored its three-run lead in the top of the eighth, scoring on a throwing error by McCann and Swisher’s RBI groundout.

The Braves broke a scoreless duel in the fifth when Francoeur went deep, his first homer since June 2.

Chamberlain knocked Kawakami out of the game with a liner that struck the Atlanta starter before he could get his glove up. The ball deflected to shortstop Yunel Escobar, who threw out Chamberlain for the third out.

Kawakami walked off the field but went straight to the clubhouse for treatment. He was day to day.