Updated

Alex Rodriguez tied Lou Gehrig's major league grand slam record Tuesday night during a six-run eighth inning that lifted the Yankees over the Braves, 6-4.

Rodriguez lined his 23rd career grand slam over the left field wall to tie the game and Nick Swisher added a two-run blast for the lead, saving CC Sabathia from another loss and leading New York to its fifth straight win, and 15th in 19 games.

Sabathia (8-3) gave up four runs and 10 hits in seven innings while striking out six and walking two. He was coming off a loss last Thursday to the Rays, the Yankees' only one in their last nine games.

Rodriguez, in his 19th season, worked a 3-0 count against Jonny Venters (3-3), then looked at a strike before fouling two pitches off. His next swing tied Gehrig, the Yankee great who played 17 seasons for the team before ALS knocked him out of the game.

"It means a lot. It's very special," said Rodriguez. "This game's very, very difficult. If you're not going to enjoy these great moments then it's not any fun.

"Gehrig's not only one of the all-time greats, but he's one of ours. He's a Yankee. He's one of those guys that if you every have an opportunity, when they say, 'Who would you take to dinner?' I mean, for me, he would be top four or five."

The Braves got a three-run double from Matt Diaz in the first inning but lost their third straight.

24-year-old lefty Mike Minor was lifted after giving up just his fifth hit, a one-out single to Derek Jeter in the eighth. Minor was charged for one run and Venters gave up four without retiring a batter.

Clay Rapada pitched around a walk in the eighth for the Yankees and Rafael Soriano struck out two in a perfect ninth for his 10th save of the season and 100th of his career.

The Yankees won the opener of the three-game interleague series 3-0 on Monday, scoring all of their runs in the first three innings. Their bats were all but silent until the eighth inning of this one.

The Yankees loaded the bases after Jeter singled in the eighth and Minor was relieved by Venters, who gave up a single to Curtis Granderson and walked Mark Teixeira.

Rodriguez's slam gave him 1,859 career runs, tying him with Mel Ott for 11th all-time. His 1,922 RBI are two shy of Jimmie Foxx for sixth place.

"It is what it is. I made a bad pitch and he crushed it," said Venters. "Like I said, it's a shame. Mike threw the ball really well and personally I felt great. I just didn't make any pitches."

Robinson Cano followed with a single, chasing Venters for Cory Gearrin, and Swisher homered two pitches later for the 6-4 lead.

Earlier, Sabathia labored in the first inning and Diaz sliced a bases-loaded double to the right field wall to score all the runners and give the Braves a 3-0 lead.

Michael Bourn had led off the inning with a single, extending his hitting streak to 12 games, while Brian McCann hit a ground-rule double and Dan Uggla walked.

Minor, in his best start this season, pitched out of a first-and-second situation in the first inning, stranded a single runner in the third, fourth and fifth and set the Yankees down in order in the sixth and seventh.

The Braves loaded the bases again in the seventh and scored a run on Jason Heyward's ground out to make it 4-0.

Game Notes

This is the first series between the teams since the Yankees took two of three at Atlanta from June 23-25, 2009...The teams will play three games at Yankee Stadium from June 18-20...The Braves are 2-3 on a nine-game homestand...The boy who caught Rodriguez's home run ball, Randy Kearns of North Carolina, presented it to the slugger and was rewarded with signed balls, a hat, a jersey and pictures. Kearns, a Yankees fan, was seeing the team for the first time.