The other Astros squad routed the Rangers, 13-6, on Saturday afternoon in San Antonio.
The Red Eagles gave the home team a stiffer challenge. The Mexican League squad turned three double plays and didn't commit an error under the bright lights of a Major League park.
Veracruz starter Tomas Solis no-hit the Astros starters through three innings. But once he was yanked for Oscar Verdugo, Houston pounced.
Dexter Fowler launched a towering solo homer to right-center field to put the Astros up to start the bottom of the fourth.
Astros manager Bo Porter said Fowler unleashed his inner Babe Ruth by calling his shot.
"I told him, 'You got one more [at-bat] this spring. Whatever you need to do, make sure you're ready,'" Porter said. "He said he was going to hit a home run. And he actually did it."
"I'm guilty, it's true," Fowler said. "I just knew I'd find a pitch to hit."
The inning was just getting started.
The Astros eventually loaded the bases with no outs, but they only managed one more run on Matt Dominguez's sacrifice fly.
That was all Oberholtzer needed. In his final tuneup before facing the Yankees on Thursday, he was as efficient as could be.
The lefty only allowed two bloop hits and struck out a pair while allowing no runs in 58 pitches and six innings.
"Definitely a foot forward, definitely a step in the right direction," Oberholtzer said. " I threw some good pitches early in the count to keep them off my fastball, and they really got themselves out. My pitch count was down and I could have gone deeper in the game, which is always positive."
Dominguez also made the lefty's night easier, snaring several difficult balls at the hot corner to showcase his Gold Glove Award potential.
There was still cause for concern for the Astros despite the split-squad status. Houston struggled to touch Solis even with a lineup that could very well double as its Opening Day club. Fowler, Jose Altuve and Jonathan Villar were the only starters to record hits.
But the bullpen couldn't have been better, as Matt Albers, Anthony Bass and Josh Fields combined to toss three scoreless innings and preserve Oberholtzer's gem.
Porter said the likely starters and Major League regulars will mostly have Sunday's game off, meaning this was their last appearance this spring.
"They'll have a complete day off tomorrow and Monday," he said. "Obviously, they'll hit in the cage, get their normal work in. But this was a good end to their spring."