The game was scoreless through four innings but Cincinnati erupted for five runs in the fifth and rode Bailey's effective outing to the victory, which evened their three-game series.
Then, after Bailey and Drew Stubbs each drew a walk, Renteria pulled a 1-0 pitch from Wandy Rodriguez (7-8) into the left field stands for a grand slam.
Bailey (6-5) limited the Astros to one run, allowing five hits while walking three and striking out four, rebounding his worst start of the year in his previous outing against the New York Mets.
Rodriguez ended up surrendering five runs on four hits before exiting after five innings.
Luis Durango drove in Houston's run.