Vazquez had been a victim of shaky run support all season, entering his start Monday owning an average of 4.24 runs per nine innings, ranking him 54th among the 68 American League pitchers with 10 or more starts this season.
That trend seemed to be continuing as Vazquez's seven innings of two-run ball were backed only by Nick Swisher's fourth-inning homer, with the right fielder connecting for a solo shot off a very sharp Jake Westbrook.
But with baserunners difficult to come by, Granderson answered the call for the thirsty Yankees with his 10th home run, a towering shot to right field off Westbrook that came with Jorge Posada aboard.
"I was just trying to extend the rally and got the ball out of the ballpark," Granderson said. "The big thing is, once you start getting balls that you're hitting hard, you've just got to continue to stay positive."
It was to the benefit of Vazquez, who continues to be one of the Yankees' most reliable starters despite numbers that remain especially skewed by an awful April.
"I'm pretty happy that I'm helping the team," Vazquez said. "That's the bottom line. After the first month, I tried to forget about it and just tried to help the team from then on."
Travis Hafner put the Indians on the board in the second inning when he connected with an 0-1 pitch from Vazquez, depositing it over the right-field wall for his ninth home run, a solo shot that was estimated at 410 feet.
"I think the biggest thing for us is that I'd rather not hit a home run and win than hit a home run and lose."
-- Alex Rodriguez
Cleveland took a sixth-inning lead against Vazquez as Shin-Soo Choo stroked a two-out double into the right-center field gap, sending Michael Brantley home standing up from first base. But that was all for Vazquez, who improved to 6-2 with a 3.05 ERA over his past nine starts.
"He changed speeds very well," Indians manager Manny Acta said. "He's been around a long time in both leagues. You can't blame our kids. The guy pitched a good ballgame."
The bullpen held it the rest of the way, with Dave Robertson inducing a big double play out of Asdrubal Cabrera in the eighth and Boone Logan coming on to retire Choo, before Mariano Rivera locked down the ninth for his 21st save.
Yankees manager Joe Girardi had said before the game that he still would lean toward Joba Chamberlain as his eighth-inning reliever, but on this night his gut told him that Robertson was the guy to go to, as he continues to weigh matchups in those situations while Chamberlain struggles.
"Sometimes the seventh inning is just as important, so I don't really see the difference," Robertson said. "I'll throw whenever he wants me to -- if he wants me to go in for the seventh, the sixth or the third. It doesn't bother me, I'll go do it."
Westbrook would be left with the loss and a hollow moral victory of silencing A-Rod, who went homerless for the fourth consecutive game as he looked to become the youngest member of the 600-homer club, batting one day in advance of his 35th birthday.
"I don't think anything changes," Rodriguez said. "I feel good up there. I don't think I'm getting any more or any less. Every time I come to the plate, there's a potential damage situation, and they know that. They're not just going to throw cookies in there for me."
Rodriguez struck out swinging in the first inning and lined into an unorthodox double play in the fourth that saw left fielder Trevor Crowe double off Mark Teixeira on a ball that the Yankees contended had been trapped.
"I just went by the reaction of the left fielder," Girardi said. "The left fielder comes up firing to second base and doesn't look to see where the runner is, that's my reaction. The players usually tell you."
With the call on the field standing, A-Rod grounded out to shortstop facing Westbrook in the seventh. Granderson's homer bought Rodriguez another turn, but after surrendering a grand slam to Rodriguez on May 31 in New York, Chris Perez won this battle by inducing a soft popup to first base.
"I went after him," Perez said. "I even threw him a hanging slider the second pitch. He took it. If there had been nobody on, I would have thrown him all heaters. I think he's starting to feel it. He's starting to get aggressive. That could be good for us. Throw a sinker down and in and let him roll over it."
Rodriguez said that he had been thrown a pitch to hit in that at-bat against Perez, but said he wasn't worried about the home run. It will come, whether it is this week, next week or next month, he said.
"I think the biggest thing for us is that I'd rather not hit a home run and win than hit a home run and lose," Rodriguez said.