Rodriguez gave up four runs in the fifth before being taken out with two outs, and Chad Paronto gave up another home run to Edwin Encarnacion, the first batter he faced in relief, upping the deficit to 7-0.
Rodriguez's pitch to Griffey was a fastball that caught the middle. He was trying to throw it away to get Griffey to ground into a double play. Griffey was 9-for-12 against Rodriguez with a double and two home runs entering the game.
"I feel my arm was very strong today," Rodriguez said. "I think it just was my throwing today. I used a lot of my fastball, and I missed sometimes on my location."
The Astros did make a sharp comeback attempt. After Hunter Pence hit a solo shot to the Crawford Boxes in the fifth, he doubled in the sixth and reached third on a throwing error by shortstop Jeff Keppinger, who erred again attempting to field a grounder by Humberto Quintero that scored Pence.
Ty Wigginton then hit a three-run, pinch-hit homer to pull the Astros within three.
"I definitely had a plan against him, I was looking for a heater, a fastball in," Wigginton said. "He threw me a first-pitch changeup and a slider away, and then he actually threw me a heater in so it worked out good."
The Reds scored again in the ninth as Brandon Phillips singled to right and stole second. An infield single by Paul Bako to Kazuo Matsui sent him home.
Houston attempted another comeback in the eight on a risky move, using Michael Bourn to pinch-hit for Quintero. Bourn, who has been out since Saturday with a sprained ankle, singled and reached third, but a double play and a strikeout ended the Astros' chances.
The Astros stranded six on nine hits as Edinson Volquez earned just one run. Miguel Tejada said the team could have been due for a slump.
"They threw the ball good," he said. "That kid, Volquez, he got through the middle of our lineup and that's why we didn't come into any big hits. We just have to give credit to the pitcher. We cannot say we're not hitting just because we're not hitting. You have to give credit to Volquez, the way he pitched."
Houston went through five relief pitchers, including Chris Sampson, who pitched two frames just three days after throwing 2 1/3.
Despite the loss, the Astros did take their second consecutive series, and fourth of their past five. But the loss snapped an eight-game streak against the Reds, dating back to May 31, 2007.
"We played another professional team, and we cannot expect to beat everybody," Tejada said. "We're just happy to take two out of three and go from there. That's what we've got to do now, we just have to go up there and try to see how many series we can win."