Oberholtzer said he told Houston manager Bo Porter that they were going to try and get through the inning.
Oberholtzer threw seven shutout innings, and L.J. Hoes scored twice to lead the Astros to a 2-0 victory against the Red Sox.
Oberholtzer (2-0) allowed four hits while walking two and striking out two.
In his first two career starts, Oberholtzer has thrown 14 scoreless innings, allowing seven hits.
He became the first Astros pitcher to throw at least 14 scoreless innings over his first two major-league starts. He is also the first major league pitcher with at least seven scoreless innings in his first two starts since Philadelphia's Marty Bystrom did it in 1980.
Oberholtzer said he told himself before the game to pound the strike zone and stay confident.
"For me, my mindset is to attack and throw strikes," Oberholtzer said. "Obviously, I am always confident. I told myself today that they were either going to get me early or not at all, so I just came out, attacked the zone, mixed it up."
Porter said Oberholtzer was tremendous.
"Even the start against Baltimore against that lineup he did a great job of mixing his pitches, getting early contact," Porter said.
"Today, against a really good hitting lineup I felt like he did a tremendous job of pitching to the inner third of the plate and really attacking from the standpoint where he didn't put himself into too many deep counts where he was forced to throw a fastball."
Hoes and Jonathan Villar each had two hits for the Astros, who snapped a four-game losing streak.
Houston took a 1-0 lead in the fifth. Hoes led off with a single and stole second and scored on a single by Robbie Grossman.
The Astros added a run in the seventh to make it 2-0.
The Red Sox, who lost for the second time in their past seven games, put runners on the corners with two outs in the eighth after a David Ortiz bloop single off Wesley Wright advanced Jacoby Ellsbury to third, but Josh Fields struck out Mike Napoli to end the inning.
Fields struck out the side in the ninth for his first career save.
"I felt pretty good," Fields said. "I was trying to be as aggressive as I could. I knew I had one run for a cushion, so I was coming right after those guys as hard as I could hoping they'd get themselves out."
Oberholtzer did not allow a hit until Dustin Pedroia's single in the fourth. He was caught stealing to end the inning.
Stephen Drew laced a two-out double to right in the fifth but was left stranded.
Boston threatened in the sixth with a two-out single by Pedroia and a walk to Ortiz, but Oberholtzer got a groundout by Napoli to second to end the inning.
Boston starter John Lackey appeared to have rolled his left ankle to end the second inning, coming off the mound for a soft chopper hit by Matt Dominguez. Lackey threw to first for the third out and hobbled off the field with a trainer and coach, but came back out for the third inning.
"I am sure you guys saw it; I rolled my ankle pretty good," Lackey said. "I've done it several times playing other sports, but it definitely didn't feel great. I wasn't going anywhere. I just taped it. I pitched fine.
"I don't think it affected the way I threw the ball or anything. They were definitely keeping an eye on me to make sure it did not affect my delivery. Nothing happened with my arm."
Lackey (7-9), who said his ankle will not affect his next start despite limping noticeably after the game, allowed two runs and eight hits with two walks and 10 strikeouts in six innings.
Lackey has lost three consecutive decisions.
"I thought John had really good stuff tonight," Boston manager John Farrell said. "He had good secondary stuff and got a lot of key strikeouts when he needed them. Oberholtzer threw the ball over the plate.
"He got ahead of us a lot and when we were able to get a chance off him -- which was not too often tonight -- he was able to get the key outs when he needed it in a couple of spots."
- Red Sox OF Shane Victorino was selected AL Player of the Week Monday for the week of July 29-August 4.
- Red Sox OF Daniel Nava will miss the three-game series against the Astros after being placed on paternity leave Monday for the birth of his daughter, Faith, who was born Monday. Boston recalled RHP Brandon Workman from Triple-A Pawtucket to take Nava's spot on the roster.
- Houston minor league pitcher LHP Sergio Escalona was suspended 50 games Monday for violating Major League Baseball's Joint Drug Prevention and Treatment Program. Escalona was pitching at Double-A Corpus Christi.
- Jordan Lyles starts for Houston against Boston's Steven Wright in the second game of the series on Tuesday.