"Anytime you can do something like that in a Yankee uniform is special," said Rodriguez, who connected off Scott Linebrink in the eighth.
A day earlier, Derek Jeter set the career hits record at Yankee Stadium, and Mariano Rivera passed Lee Smith for second on the saves list on Monday.
That's about all Yankees fans have had to root for as the club plays out the final week at Yankee Stadium with the likelihood they will be eliminated from the playoffs for the first time since 1993 before Sunday's finale at the House that Ruth Built.
"Obviously you come into each and every season to win a World Series," Rodriguez said. "We have a lot of work to do."
Phil Hughes gave New York something positive to think about heading into the offseason, pitching four solid innings in his first start for the Yankees since April 29.
"Obviously, when a player comes back up he wants to show you what he can do. The big thing is being able to relax, and in the tough situations he made the big pitches," Yankees manager Joe Girardi said.
Jermaine Dye had an RBI groundout off Hughes in the third, but that was all the White Sox could muster against the 22-year-old right-hander and four relievers. The White Sox maintained their 2½ game lead over Minnesota, which lost to Cleveland.
"We didn't hit well today. We got a couple of men on second base with no outs and didn't hit them over," White Sox manager Ozzie Guillen said. "If we want to win we've got to score more than one run. We've got to be better out of the bullpen if we want to win this thing."
With his homer in the eighth inning, A-Rod became the first player to have at least 35 in 11 consecutive seasons (1998-2008), snapping a tie with Sammy Sosa (1995-2004).
Rodriguez has 101 RBIs this year.
Ruth, who also has 12 seasons with 35 homers, had at least 35 homers and 100 RBIs for the Yankees 11 times in the 1920s and 30s.
"The 11 years in a row means more than the numbers," said Rodriguez, who struck out in five of his previous 10 at-bats before the homer.
Johnny Damon hit a two-run homer, Robinson Cano had three hits and Xavier Nady had a tying RBI single, scoring Rodriguez, in the seventh inning. Nady then scored on a wild pitch as New York rallied against rookie Clayton Richard.
Guillen said he would keep Richard, who came in 2-4 with a 6.94 ERA, on a very short leash, and the 25-year-old rookie Richard earned every inning.
He induced double-play grounders in the first, after a leadoff walk, and in the third, after a leadoff single, and struck out Derek Jeter in the fifth after giving up two singles to start the inning.
"He was doing some funky things with the ball and we couldn't figure him out," Damon said of Richard.
But Guillen left him in a batter too long. After a visit to the mound that left Richard with a big smile, the rookie gave up a tying single to Nady. Cano followed with a double down the right-field line to end the rookie's night.
"It was definitely a step in the right direction individually," Richard said. "Late in the game there were a couple of pitches left up. I just didn't get the job done."
Mike MacDougal relieved and threw a wild pitch that allowed Nady to score and give the Yankees a 2-1 lead.
Damon hit a two-run homer in the eighth off Linebrink and Rodriguez lined his 553rd homer to right two batters later for a 5-1 lead.
Hughes' return to the mound was cut short after just four innings. Considered a future ace by the Yankees, Hughes earned a spot on the staff out of spring training. But he went 0-4 with a 9.00 ERA before sustaining a stress fracture in a rib, and he hadn't pitched since April 29. Manager Joe Girardi was hoping to see him show better command of his fastball Wednesday.
Wearing glasses instead of contacts and No. 65 - his old number - instead of 34, which he wore to start this season, Hughes needed 33 pitches to get out of the first inning. He threw 89 pitches - 57 strikes - overall. The 22-year-old right-hander gave up a run and four hits and two walks. He struck out four.
"A little bit of jitters, exciting, it's been so long, but it was a good feeling," said Hughes, who will pitch in the Arizona Fall League to build his innings.
The Yankees bullpen pitched five scoreless innings in relief.
Phil Coke pitched two-plus innings, Brian Bruney came on with a runner on second in the seventh and got three straight outs. Joba Chamberlain worked the eighth before Edwar Ramirez got the final three outs.
Notes: White Sox left-fielder Carlos Quentin had the soft cast removed from his broken right wrist, and began range of motion exercises. He is scheduled to join the team in Kansas City on Friday, where he will swing a bat. ... A-Rod had struck out in five of his previous 10 at-bats before the home run.
