The Marlins will counter with right-hander Carlos Zambrano, who has pitched well for them, but with little to show for his efforts.
Rodriguez is 3-2 with a 1.64 ERA in his first six starts this season. He is 3-3 with a 3.18 ERA in his career against the Marlins.
Rodriguez's last start on Wednesday was cut short after 90 pitches because Astros manager Brad Mills took a cautious approach with the left-hander pitching on short rest.
Rodriguez was pitching on just four days rest to fill the rotation gap caused by Kyle Weiland's shoulder injury.
Mills does not want his team to read too much into Sunday's 8-1 loss to the Cardinals, or the five-game winning streak that preceded it.
"I think we need to focus on what we need to do tomorrow and keep going from there and the rest of this homestead," Mills said Sunday. "We can't let too many things out of our control get too far ahead of us. These guys have done a good job of doing that, keeping their focus on the now. Let's keep that."
Zambrano had a no-decision at San Francisco on Wednesday in his last start.
He gave up no runs and five hits in seven innings and he was in line for the win, but Miami was unable to hold the lead in the ninth.
In three of his first five starts, the Marlins led in the ninth but were unable to preserve the edge.
Zambrano says he isn't worried about his personal stats.
"It's not like I'm going to go through the season without a win," Zambrano said. "The key is, I'm throwing strikes."
Zambrano has been one of the most pleasant surprises for the Marlins. In five starts, he has a 2.53 ERA.
Don't expect the old, volatile Zambrano to resurface, he said.
"Actually, I feel like I'm a new Carlos Zambrano, because the old Carlos Zambrano would be throwing a chair and screaming at his teammates," he said Sunday.
Marlins: Stanton extends streak
In addition to his bases-loaded walk in the eighth inning, which drove in the go-ahead run Sunday, Giancarlo Stanton went 1-for-3, giving him a season-high nine-game hitting streak.
Omar Infante's second-inning double on Sunday extended his hit streak to four straight, and he's had a hit in 10 of his last 12 games.
Hanley Ramirez is 7-for-18 (.389) against Rodriguez.
Astros: Rodriguez ranks high among left-handers
Since 2009, Rodriguez ranks second in the NL in ERA (3.26) by left-handers, behind only Clayton Kershaw (2.63).
Carlos Lee is 26-for-70 (.371) with five homers and 16 RBIs lifetime against Zambrano
Second baseman Jose Altuve is hitting .352 after going 2-for-4 Sunday.
Zambrano is no stranger to Minute Maid Park, where in 18 appearances (16 starts) he is 9-4 with a 3.57 ERA.
For his career, he is 16-8 with a 2.69 ERA against the Astros.