The right-hander would like to have one pitch back from his third major league start, a 4-3 loss to the Texas Rangers.
Tropeano (1-2) gave up a bases-loaded triple to Rougned Odor with two outs in the third inning Monday night, and the Rangers never trailed.
"Overall, it felt good. My command was a little bit better today than it has been in the past, since I've gotten called up here," Tropeano said. "I just threw one pitch — it was down, middle — and he put a good swing on it. I should have buried it in that count. ... It was down, just not down enough."
Rodriguez, who had played 13 seasons and 1,095 games in the minors before getting called up earlier this month, had his first two major league hits.
Rodriguez was the second of three consecutive Rangers to reach base in the third before Odor's triple into the left-center gap. Rodriguez then had a tiebreaking single in the seventh after Houston intentionally walked Robinson Chirinos.
Tropeano allowed four runs on five hits, with three strikeouts and two walks.
"He's learning. He's facing hitters he's never seen before. He's competing out there. He's making his pitches and doing a nice job," Astros interim manager Tom Lawless said. "He's seeing what it is like up here. He's been able to compete. The one difference is that he's into too many deep counts right now. Trusting his fastball more would help him. That's what he's learning. He's gotten better start one to start three."
Texas won for the ninth time in its last 10 games to get its 63rd win overall, ensuring that the Rangers will avoid their first 100-loss season since 1973.
"It puts a big smile on my face, just to know there's no three digits in our loss column," said interim manager Tim Bogar, who is 10-6 since Ron Washington resigned. "But other than that, we know as an organization we're not a team that's a 100-loss team. We're not heading in the wrong direction. It's just a little bump in the road for us."
The Astros got even in the sixth after a leadoff double by Jonathan Villar before an error by Rodriguez at third base. Jose Altuve then had an RBI double, his major league-best 221st hit, and Chris Carter hit a sacrifice fly to deep right.
Houston's first run came in the fifth when Jake Marisnick had a leadoff single and scored after a wild pitch and two groundouts.
Derek Holland (2-0), who pitched into the eighth, had escaped unscathed after giving up leadoff hits in each of the first two innings. The Rangers turned a double play in the first and Holland picked off Marisnick in the second.
Marisnick also turned in an incredible catch in right, reaching up and making a running grab to rob Adrian Beltre of extra bases in the eighth inning.
Rangers: 2B Jurickson Profar, who has missed all season because of a muscle tear in his right shoulder, won't play in the Arizona Fall League as expected after having more problems. Profar was back in Texas to see Rangers team physician Dr. Keith Meister after meeting in the last week with at least two other doctors.
The second game of a three-game series between the bottom two teams in the AL West, with left-hander Brett Oberholtzer (5-12) going for the Astros against Texas rookie right-hander Nick Martinez (4-11), who has a 2.74 ERA over his last four starts.