And as Rodriguez's pursuit of that milestone blast moves to a new city, he is reminded that there's a whole lot of good baseball going on outside his at-bats. Rodriguez went homerless on Thursday, but the Yankees rode a seven-run seventh inning to an 11-4 pounding of the Indians.
"I'm not going anywhere," Rodriguez said. "We're right in the middle of a pennant race. I think the key is that we're being productive and winning."
New York took three out of four games in the series at Progressive Field, which featured large walkup crowds hoping to catch a piece of history.
Rodriguez had three opportunities with the bases loaded against Cleveland on Thursday and got to bat twice in the seventh inning alone, finishing the evening 1-for-4 with three RBIs. Since clubbing No. 599 a week ago in New York, he is 9-for-30 (.300) with seven RBIs, going 34 plate appearances without a long ball.
"I guess we'll talk about it again tomorrow, unless something happens overnight," manager Joe Girardi said. "He had good at-bats and drove in runs for us. We all hoped it would happen here, but it didn't, so we move on to the next city."
One issue that Girardi does not need to discuss further is the status of his spot starter, right-hander Dustin Moseley, who limited the Indians to one run in six innings and has earned another turn in the rotation.
Filling in for the injured Andy Pettitte after a one-start audition by Sergio Mitre, Moseley pitched out of trouble in the first inning -- allowing only an Austin Kearns sacrifice fly -- before holding Cleveland scoreless through the next five frames, ending his night after 83 pitches.
"There was a lot going on," Moseley said. "You're excited to get out there and get a start. Maybe I was pressing a little bit, trying to do too much, but I got to sit on the bench a little bit and go through the process of [saying], 'All right, what do I have to do to be successful?' And it's throwing strikes."
It was a tighter contest when Moseley departed, backed by only two runs thanks to an A-Rod sacrifice fly in the third inning and Derek Jeter's RBI single in the sixth. But even that would prove to be enough to give Moseley the victory in his first start since April 17 of last year, when he was with the Twins.
"I'm really excited," said Moseley, who underwent arthroscopic surgery on his left hip last August. "It's been kind of a long road, these last couple of years. To get a start, go out there and keep the team in the game and eventually get a win, it worked out real good for me."
The Yankees saw a total of 233 pitches from Cleveland hurlers, although only 42 of them were from starter Mitch Talbot, who was forced to exit after two-plus innings with a mid-back strain, charged with a run on a hit.
Losing pitcher Frank Herrmann allowed a run in the sixth inning, but it was in the seventh that the Yankees did most of their damage, as Tony Sipp was charged with three runs and Joe Smith with four, pacing a pitching staff that walked 12 on the night.
Robinson Cano belted his 20th homer, a solo shot off Sipp, marking blasts in back-to-back games. Both Curtis Granderson and A-Rod added two-run doubles to highlight the barrage, though New York left a season-high 14 runners on base in the victory.
"Innings two through five, we had first and second four times with nobody out and we hit a lot of line drives," Girardi said. "I can't fault guys for their at-bats, because we were hitting the ball hard. We just weren't having a lot of luck. They stayed after it."
Dave Robertson hurled a scoreless seventh and, with the outcome well in hand, Chan Ho Park was called upon for the final six outs. He allowed three runs (two earned) on two hits but recorded a strikeout of fellow Korean Shin-Soo Choo.
"It was pretty exciting to face Choo," Park said. "The last four games, everybody paid attention in Korea. They want to see me face him. ... We had lunch today and talked about a lot of things besides baseball. It was good. I'm very proud, and [Choo] makes Korean people proud as a hitter and successful player."
The Tribe, meanwhile, entrusted their ninth inning to infielder Andy Marte, who hurled a scoreless frame that included a strikeout of Nick Swisher, who had coincidentally pitched a scoreless inning in a blowout loss last April for the Yankees at Tropicana Field.
"Like the guys say, you've got to just wear it," Swisher said. "Me and Marte, we've both got the same ERA. I now have a new most embarrassing moment."
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.