CLEVELAND (AP) -- Yankees fans got two big home runs from their favorite team - just not the one they really came out to see.
Nick Swisher also homered for New York, now 16-5 in July.
" It was big because it helped my team,'' Granderson said. " I was just trying to keep the inning going, got it up in the air and it went out."
Granderson connected with one out in the eighth inning off Jake Westbrook (6-7), who held Rodriguez hitless in three at-bats and was clinging to a 2-1 lead. Jorge Posada reached on a one-out single before Granderson delighted a large portion of the crowd of 27,224 hoping to see homer history.
Indians manager Manny Acta said he didn't want to bring in a reliever to face Granderson, who homered twice on Sunday.
" I wouldn't even think about taking out a guy who had a two-hitter in the eighth,'' Acta said. " I don't second-guess myself. I'm not flipping coins in the dugout."
The normally mild-mannered Westbrook kicked the mound, grabbed the resin bag and fired it to the ground as Granderson circled the bases.
" That was the ballgame,'' Westbrook said. " A two-run home run when you're up a run in the eighth, that's what I'm upset about."
Rodriguez popped out to first in the ninth on perhaps the best pitch he had to hit all night, a fastball by reliever Chris Perez , and finished 0 for 4.
He wasn't upset that he failed to hit the homer, though.
" I'd rather not hit a home run and win then hit a home run and lose,'' Rodriguez said. " It's going to come whether it's this week or next week or next month. The big point for me is to stay within the game."
Shin-Soo Choo put Cleveland ahead 2-1 in the sixth with an RBI double off Javier Vasquez (9-7). Travis Hafner hit a solo homer in the second. It was the designated hitter's fifth straight hit.
Vazquez gave up two runs and five hits over seven innings, improving to 6-2 in 10 starts since June 1. He left after walking Michael Brantley to open the eighth. David Robertson and Boone Logan finished that inning and Mariano Rivera worked the ninth for his 21st save in 23 chances.
" I wanted to stay in, but their lefties were coming up and the bullpen came in a did a great job," Vasquez said.
Rodriguez went homerless for the fourth consecutive game as he tries to become the seventh player and youngest to reach the 600 milestone. He returned to the lineup after he was hit in the hand by a pitch in the eighth inning Sunday and was removed for a pinch runner.
After striking out his first time up against Westbrook, the Yankees third baseman had an apparent single turned into a bizarre double play in the fourth by third base umpire Jerry Meals.
With Mark Teixeira on first and one out, Rodriguez hit a sinking liner that appeared to touch the ground before going into the glove of left fielder Trevor Crowe . Teixeira saw it that way and was pointing to the ground and saying the ball had been trapped as he stood on second base. Meals, however, ruled it a catch and when second baseman Jason Donald took Crowe's throw and tagged Teixeira, the inning was over.
Yankees manager Joe Girardi argued, but the call stood. TV replays showed the ball appeared to hit the turf.
" I went by what their left fielder did,'' Girardi said. " When he came up throwing, that tells you something.
" It's a tough call. Some go your way, some don't," Girardi said.
The Yankees also came within inches of scoring in the fifth but got nothing. Posada drew a one-out walk and Granderson followed with a drive off the top of the wall in right, just missing a homer. Right fielder Choo grabbed the ball on the rebound and threw to second, where Granderson was called out by second-base ump Dale Scott. Replays showed Granderson was safe, though nobody argued.
Swisher tied it with one out in the fourth with New York's first hit, a drive into the right-field seats for his 18th homer.
Westbrook, perhaps making his final start in a Cleveland uniform, gave up three runs and four hits over eight innings. The Indians could deal the high-priced veteran before Saturday's trading deadline.
Rodriguez will try for his milestone hit Tuesday on his 35th birthday, against right-hander Josh Tomlin, scheduled to make his major-league debut.
" Just pitch to him,'' Acta said. " I couldn't care less if he hits three home runs tomorrow and we win. We're not going to base our whole game plan on trying to stop him. He's going to hit it sooner or later."
NOTES: Cleveland went 0 for 5 with runners in scoring position and is 1 for 31 in its last five games. ... Girardi said RHP Dustin Moseley will start Thursday. He'll replace RHP Sergio Mitre , who allowed seven runs (five earned) over 4 1-3 innings Saturday in the rotation spot vacated by LHP Andy Pettitte (strained groin). ... Indians RHP Kerry Wood (blister) will throw a bullpen session Tuesday. He hasn't pitched since July 11. ... Indians RHP Anthony Reyes (elbow) will make a minor league rehab start at Double-A Akron on Tuesday. He had surgery in June 2009.