The Atlanta Braves drafted Oberholtzer in the eighth round in the 2008 Major League Baseball draft, and assigned him to the RookieGulf Coast League Braves. In ten relief pitching appearances, he posted a 4–1 win–loss record, 2.89 earned run average, and 32 strikeouts in 37 innings pitched. In 2009, Oberholtzer was assigned to the Appalachian League's Danville Braves, where he made the first 12 starts of his professional career. On July 6, 2009, he was named the Appalachian League's pitcher of the week. In 67 total innings, Oberholtzer went 6–2 with a 2.01 ERA and 56 strikeouts. He made his full-season baseball debut in 2010, splitting the season between the Class-ARome Braves and the Advanced-AMyrtle Beach Pelicans. In 26 combined appearances, 22 of which were starts, Oberholtzer pitched to a 6–8 record, 3.78 ERA, and 126 strikeouts in 135 innings. In 2011, Oberholtzer was assigned to the Double-AMississippi Braves, where he won the Southern League's pitcher of the week award on July 25 and was named a mid-season All-Star. With the Braves, he posted a 9–9 record, 3.74 ERA, and 93 strikeouts.
Houston Astros
On July 25, the Braves traded Oberholtzer to the Houston Astros, with Juan Abreu, Paul Clemens, and Jordan Schafer, for Michael Bourn. Oberholtzer was assigned to the Double-A Corpus Christi Hooks for the remainder of the 2011 minor league season, and pitched to a 2–3 record, 5.27 ERA, and 28 strikeouts. He split time in 2012 with Corpus Christi and the Triple-AOklahoma City RedHawks. In a career-high 166 innings pitched, Oberholtzer posted a 10–10 win–loss record, 4.37 ERA, and 137 strikeouts. Oberholtzer made his Major League debut on April 21, 2013. He made his first career start and got his first career win against the Baltimore Orioles, on July 31, 2013. During his tenure with the Astros in 2013, he appeared in 13 games going 4-5 with a 2.76 ERA and 45 strikeouts. With Triple-A Oklahoma City in 2013, Oberholtzer pitched to a 6–6 record in 16 starts, with a 4.37 ERA and 72 strikeouts. Oberholtzer made 24 starts with the Astros in 2014, and five in Triple-A. With Houston, he went 5–13 with a 4.39 ERA and 94 strikeouts in 143 innings. In his five minor league starts, Oberholtzer posted a 1–2 win–loss record with a 4.65 ERA and 31 strikeouts in 31 total innings. Oberholtzer battled a blister on his left index finger early in the 2015 season. He was placed on the disabled list on March 31, and activated in May. He was pulled from his first start after three inning when the blister recurred, and went on the disabled list once again. On June 27, after giving up 6 runs in 1 1/3 innings to the Yankees, after surrendering a home run Oberholtzer was immediately ejected when he intentionally threw at Yankee third baseman Alex Rodriguez; although Oberholtzer said it was inadvertent, immediately after the game the Astros sent him to Triple-A. He would make just eight starts for the Astros in 2015, going 2–2 with a 4.46 ERA and 27 strikeouts in 38 innings. With the Triple-A Fresno Grizzlies, Oberholtzer went 7–4 in 12 starts, with a 3.86 ERA and 52 strikeouts in 70 total innings.
Philadelphia Phillies
On December 12, 2015, the Astros traded Oberholtzer, Mark Appel, Vince Velasquez, Tom Eshelman, and Harold Arauz to the Philadelphia Phillies for Ken Giles and Jonathan Arauz. He was designated for assignment on August 6, 2016. With the Phillies, Oberholtzer pitched to a 2–2 record, 4.83 ERA, and 38 strikeouts in 26 relief appearances.
Los Angeles Angels
The Los Angeles Angels claimed Oberholtzer off waivers on August 9, 2016. He made 11 appearances for the Angels, posting a 1–1 record, 8.55 ERA, and 16 strikeouts in 20 total innings.
On December 7, 2016, Oberholtzer signed a minor league contract with the Toronto Blue Jays. He was added to the active roster on July 31, 2017, and designated for assignment the following day to make room on the roster for Nori Aoki. On October 13, Oberholtzer elected free agency.
Somerset Patriots
On April 4, 2018, Oberholtzer signed with the Somerset Patriots of the Atlantic League of Professional Baseball.
On April 24, 2018, Oberholtzer signed a minor league contract with the Colorado Rockies. He elected free agency on November 2, 2018.
Somerset Patriots (second stint)
On February 19, 2019, Oberholtzer signed with the Somerset Patriots of the Atlantic League of Professional Baseball.
Chinatrust Brothers
On July 27, 2019, Oberholtzer signed with the Chinatrust Brothers of the Chinese Professional Baseball League. He became a free agent following the season.
Somerset Patriots (third stint)
On February 17, 2020, Oberholtzer signed with the Somerset Patriots of the Atlantic League of Professional Baseball.
