Latos, who is 7-3 with a 4.33 ERA, had a 15-start unbeaten streak, which included seven winning decisions, come to an end on Wednesday in a 7-1 loss to the D-backs when he gave up two home runs to Jason Kubel and lasted just 4 2/3 innings.
Rodriguez (7-8, 3.75 ERA) gave up four hits and five earned runs while working four innings on Wednesday in an 8-4 loss to the Padres.
The loss to the D-backs was Latos' first since April 18, and the unbeaten-start streak included three games in which the Reds' bullpen blew saves after the 24-year-old right-hander exited the game.
Despite the loss to the D-backs, the Reds are 11-5 in Latos' last 16 starts.
Latos wasn't happy with his performance against the D-backs, throwing his glove as he reached the dugout after coming out of the game.
"If you throw pitches right down the heart of the plate to Major League hitters, they're going to hit the ball hard," Latos said when asked about the home runs Kubel hit.
Astros manager Brad Mills wants Rodriguez to focus from the first pitch against the Reds.
"The biggest thing from the last couple of starts is that we want him to get going from pitch No. 1," Mills said. "Right when he gets out there, we want him to attack the hitters.
"His stuff is good. He doesn't have to be perfect. He needs to attack hitters. So many times we have talked about guys struggling with their command because they try to dance around the zone a bit. We want him to be able to attack guys a little bit, and we'll go from there."
Rodriguez has been mentioned as a pitcher who might be traded to a contender before the July 31 non-waiver Trade Deadline, and his pitching coach, Doug Brocail, thinks the trade talks have distracted him.
Rodriguez has gone 3-4 with a 5.65 ERA in his last 10 starts after going 4-4 with a 2.14 ERA in his first 10 this season.
"He gets a little nervous about that. I try to tell him it's nothing you can control," Brocail said. "But I see it because I'm with him every day and talk to him every day. "I just think that lately his mind's been elsewhere, and we need to work on that. He still throws the same velocity, still throws his curveball and changeup."
Reds: Chapman piling up strikeouts
Reliever Aroldis Chapman, who has 27 strikeouts in his last 34 outs, recorded his 17th save on Sunday, working a scoreless ninth inning while striking out two and walking one.
Astros: Altuve a young star
At 22 years old, Jose Altuve was the second-youngest member of the NL All-Star squad. Nineteen-year-old Nationals rookie Bryce Harper was the youngest All-Star.
Altuve, who was hitting .293 with five home runs and 27 RBIs before Sunday's game, is also the second-youngest All-Star in Astros history, behind Cesar Cedeno, who was 21 when named the NL's starting center fielder in 1972.
Through 95 games, the Reds have used only five starting pitchers: Bronson Arroyo, Homer Bailey, Johnny Cueto, Latos and Mike Leake.
The streak is a modern franchise record, the longest since the 1898 staff of Still Bill Hill, Pink Hawley, Frank Dwyer, Bill Dammann and Ted Breitenstein made every start through the first 147 games.