Liberatore is of Italian descent and attended Quigley Catholic High School in Baden, Pennsylvania, for three years, and transferred to Blackhawk High School in Chippewa Township, Pennsylvania, for his senior year. He pitched 6 innings as a senior and graduated from Blackhawk in 2005. He played for the American Legion team after his senior year and the coach thought he was more comfortable in the outfield than at pitcher. In the summer of 2005, he received a scholarship attend Tennessee Technological University and play college baseball for the Tennessee Tech Golden Eagles. Liberatore appeared in only six games and made one start as a freshman, while allowing twelve earned runs in 10 innings. In 2007, as a sophomore, he appeared in 15 games with four starts and an 8.42 earned run average and as a junior he had an 8.68 ERA in 13 appearances. He participated in the Valley Baseball League over the summer between his junior and senior seasons and won the pitcher of the year honors while leading the league with a.170 batting average against. In 2009, he was 2-0 with a perfect 0.00 ERA in three starts, with 21 strikeouts when he left his last game with a season-ending elbow injury. Liberatore underwent Tommy John surgery and received a medical redshirt season. In 2010, as a redshirt senior, he was 6-4 with a 5.30 ERA in 13 starts.
On November 20, 2014, Liberatore was traded to the Los Angeles Dodgers, along with Joel Peralta, in exchange for Jose Dominguez and Greg Harris. He was also added to the Dodgers 40-man roster. At the conclusion of spring training, he was optioned to the AAA Oklahoma City Dodgers. Liberatore began the 2015 season with the Oklahoma City Dodgers of the Class AAA Pacific Coast League. The Dodgers called him up to the major leagues for the first time on April 17, 2015. He made his debut by pitching the ninth inning against the Colorado Rockies that night, retiring all three batters he faced. Liberatore pitched in 39 games for the Dodgers with a 2–2 record and 4.25 ERA. He also pitched in 19 games for Oklahoma City, with a 3.74 ERA. On July 9, 2016, Liberatore set a Dodgers franchise record with his 24th consecutive scoreless appearance, breaking the mark previously set by John Candelaria in 1991. In 2016, he appeared in 58 games with a 3.38 ERA. He underwent left elbow debridement surgery after the season. Liberatore was again optioned to Oklahoma City to begin the 2017 season. After pitching in six games in the minors, he was recalled to the Dodgers on April 23. He was sidelined with a groin injury in May and then came down with left forearm tightness shortly afterwards. That injury wound up keeping him on the disabled list for the rest of the season. He only pitched 3 innings over four games for the Dodgers in 2017, allowing one run on three hits. On May 4, 2018, against the San Diego Padres at Estadio de Béisbol Monterrey, Liberatore was one of four pitchers involved in a combined no-hitter as the Dodgers won 4–0, pitching the ninth inning to finish off the game. The Dodgers designated him for assignment on August 31, 2018 and released him on September 5. In 17 major league games in 2018, he allowed four earned runs in 13 innings for a 2.77 ERA.
