Each of Rodriguez's five at-bats -- two of which featured hits, none of which was a home run -- drew the attention of the crowd, which hustled into position in the left- and right-field seats, hoping to catch a piece of history.
Burnett's dominance ensured there was no such excitement on the Cleveland side, pitching well for the fourth time in five efforts and limiting the Tribe to seven hits over 6 1/3 innings, walking three and striking out seven to pick up his ninth victory.
"He threw the ball extremely well," Yankees manager Joe Girardi said of Burnett. "The first five innings, they got the leadoff guy on and never scored. He was really, really good out of the stretch. I thought he had a good breaking ball and fastball tonight."
Burnett has strung together a pair of good starts after his outburst on July 17 against the Rays at Yankee Stadium, when he suffered lacerations to both palms by pounding a clubhouse door and was forced to leave his start after just two innings.
"We're really happy with what he's done," Girardi said. "He's throwing the ball well. That was an unfortunate situation that happened, [but] it happened. You move on, and I think he's done a good job of putting it behind him."
On Wednesday, Burnett discovered better tempo and the ability to throw his curveball for strikes against the Indians' lineup, which the right-hander said makes a huge difference for him.
"You can ask the guys in this room -- 'When A.J. doesn't have his curveball, it's going to be a tough night,'" Burnett said.
Not this time, though. Since that encounter with the door, Burnett has hurled 11 1/3 scoreless innings against the Royals and Indians.
"I guess it's just doing my job, knowing that my job is executing the pitches that I can until skip takes me out of there," Burnett said. "It's just, 'Get back on the mound, and let's go.'"
That rhythm was frustrating for the Indians, who had their opportunities but were stifled at each turn.
"Every time we tried to get something going, A.J. stepped it up and made big pitches," Indians manager Manny Acta said. "He had an electric fastball and a good breaking ball. We had traffic, but we couldn't get that big hit."
After Burnett left at 114 pitches, Joba Chamberlain mopped up by recording two outs in the seventh and Sergio Mitre hurled a scoreless eighth for New York, which matched a season high by improving to 28 games over .500.
Rodriguez's quest for his 600th homer went unfulfilled for a sixth game, but the Yankees swung the bats plenty, as every New York starter logged a hit except for Derek Jeter (0-for-5).
The Yankees battered the All-Star Carmona early and often, chasing the right-hander after just 2 2/3 innings to the tune of 10 hits and seven earned runs.
A-Rod started the damage with a run-scoring single in the first inning, part of a 2-for-5 evening. New York scored three times in the second inning, with Mark Teixeira stroking a two-run single and Brett Gardner contributing an RBI hit.
"We did a good job," Girardi said. "[Carmona has] got a great sinker. Our guys did a good job; Alex started it after Tex doubled in the first, hitting the ball up the middle. I think we did a nice job keeping pressure on him."
New York batted around in the third inning for three more runs as Carmona was sent to the showers, with Curtis Granderson knocking an RBI triple, Gardner driving in a run with a double and Nick Swisher adding an RBI single.
Robinson Cano added a solo home run, his 19th, off rookie right-hander Hector Ambriz in the fourth inning.
"I think the key for us is swinging at strikes," Rodriguez said. "After the first two innings, [Carmona] had 40-plus pitches, and that's always a key for us, seeing as many pitches as we can. Even when we make outs, [we] make productive outs."
With the lead well in hand, the Yankees were permitted to follow along with ease as A-Rod continued to chase history, a pursuit that was postponed for yet another night when New Jersey product Frank Herrmann retired Rodriguez in the eighth inning on a 10-pitch at-bat.
"He had some good swings," Girardi said. "It's going to happen. Until it does, we'll continue to talk about it. Tomorrow would be a good day."