The left-hander likely will have another simulated outing Friday or Saturday, and if all goes well, he could be activated from the disabled list in time to start the May 7 game with the Nationals.
"He looked good; he felt good," manager Cecil Cooper said. "He used his fastball, two-seamer, changeup; he threw his curveball. He said he was locating pretty good."
"The last two pitches I felt it a little bit, but I felt a lot better," Rodriguez said.
Rodriguez will throw 75 pitches in his next simulated outing.
"We'll reassess it after that," Cooper said. "If he's good to go, we'll probably pencil him in to go [May 7]."
Rodriguez has been on the disabled list since April 20 with a strained left groin.
Also, Ty Wigginton began a three-game rehab assignment with Triple-A Round Rock on Monday, but this wasn't the type of game he envisioned as he worked to get his timing back at the plate.
Wigginton, out with a fractured left thumb, was hit in his first two plate appearances, tripled, grounded out and was intentionally walked in his final at-bat.
The third baseman will make two more appearances with the Express before rejoining the Astros on Friday.
Alyson Footer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.