Oberholtzer carried a shutout into the sixth inning before giving up a home run to Francisco Lindor and back-to-back doubles to Michael Brantley and Ryan Raburn to get lifted from the game. He allowed three runs and seven hits to fall to 0-4 lifetime against the Indians.
"I thought Obie did a good job," Astros manager A.J. Hinch said. "Early was very sharp and worked very efficiently. The ball was middle to Lindor for the home run, and then a couple of extra-base hits. I thought he gave a good effort and had a good changeup tonight. Mixed in his breaking ball. His fastball inside looked like it surprised some of the righties. Good outing for him. Unfortunately, we didn't reward him, give him any breathing room. But I'll take that outing from Obie."
Oberholtzer said he wasn't as sharp as he could have been. He only walked one batter, which is the norm for him, and he threw 54 of his 86 pitches for strikes.
"I was able to throw some good located fastballs into righties which helped me out through the first five," Oberholtzer said.
When asked about the Rodriguez incident, Oberholtzer chose not to look back.
"Yeah, I just try to take it one day at a time," he said. "Today was the day I just got the call to pitch, so I went out there and tried to give my team an opportunity to win. We came up short, but it was close."
The bottom of the Astros rotation remains in flux with rookies Lance McCullers and Vincent Velasquez likely not pitching regular schedules in the second half because of their workload and Scott Feldman still out with an injury.
Oberholtzer figures to be in the mix to help stabilize things, but he wasn't in the mindset to talk about the big picture and how he might fit into the Astros' plans in the second half.
"Whenever I get the call to pitch, I go out there and pitch," he said.
Brian McTaggart is a reporter for MLB.com and writes an MLBlog, Tag's Lines. Follow @brianmctaggart on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.