Alex Rodriguez reversed a tumultuous month of jeering with a two-run homer in the 12th inning yesterday, rallying the Yankees to a 4-3 victory over the Atlanta Braves.

A-Rod began his joyous trot around the bases by clapping his hands and blowing a kiss to the sky and, with his teammates gathered at home plate for the celebration, he flung his batting helmet high in the air.

After Marcus Giles put Atlanta ahead with a solo shot in the top half, Rodriguez finally delivered the big hit demanding Yankees fans have been clamoring for all month. The highest-paid player in baseball has been booed constantly during a difficult June, and it was beginning to wear him down.

“That’s the fans’ privilege,” Joe Torre said. “We don’t pay the fans’ salary. But right now, the fans love him to death.”

Rodriguez was thrilled with the turnaround.

“I was happy,” he said. “We needed that. I needed that. I was excited. I know the boys are waiting on me. The boys know what I can do and I was happy to come through for them.”

Rodriguez, the 2005 AL MVP, was the league’s player of the month in May when he batted .330 with eight homers and 28 RBI. But he struggled terribly in June and was locked in a 2-for-20 slump before he connected on a 3-1 pitch from Jorge Sosa (2-10) following a walk to Jason Giambi with one out.

It was Rodriguez’s 16th homer of the season, the 445th of his career, and his 100th in a Yankees uniform.

Ron Villone (1-1) escaped a bases loaded jam in the top of the 12th to keep the Yankees within one. Giambi homered earlier for the Yankees, and Rodriguez finished with three RBI.

Giambi tied the game for New York in the eighth with his 23rd homer on the first pitch he saw from reliever Ken Ray. It was the sixth time the Braves’ bullpen has blown a lead in games started by John Smoltz.

Giles hit his fifth home run on a 3-2 pitch from Scott Proctor, but the struggling Braves dropped two of three in the series to fall to 5-21 in June.

What began as a tense pitchers’ duel between Smoltz and Chien-Ming Wang turned into a battle of the bullpens – a weakness all season for the Braves.

Smoltz, who came out of his previous start Friday in the second inning with a strained right groin, lasted seven innings this time and left with a 2-1 lead.

“The leg kept me cautious,” he said. “I stayed back on the mound. I have to put us in a position to win, which I did.”

Trailing 2-0, the Yankees nicked Smoltz for a run in the sixth. Singles by Melky Cabrera and Giambi put runners at first and third with one out. Rodriguez hit a ball up the middle that deflected off Smoltz to Giles at second for an RBI groundout.